QB abstracts compiled 160613

Quantum
and Beyond
June 13–16, 2016
Linnaeus University • Växjö, Sweden
Abstracts
image: cc-by-sa-3.0, commons.wikimedia.org/wiki/file:campanil_ascendiendo.jpg
The 17th Växjö conference on Quantum Foundations
pgname
title
contact
1 Abramsky, Samson
Quantifying Contextuality
2 Akhmeteli, Andrey
No Drama Quantum Electrodynamics?
University of Oxford, United Kingdom
samson.abramsky@gmail.com
3 Appleby, Marcus
Number theoretic features of a SIC
4 Baladron, Carlos
At the crossroads of de Broglie-Bohm theory,
quantum information reconstructions and time-symmetric quantum mechanics
5 Barukcic, Ilija
6 BenDaniel, David
7 Bengtsson, Ingemar
8 Brange, Fredrik
9 Buscemi, Francesco
Anti Bohr. Quantum Theory And Causality
Implications of Einstein-Weyl Causality on
Quantum Mechanics
SICS – A grand question full of details
Minimal Entanglement Witness From Current
Correlations in Solid State Conductors
Thermodynamics as Statistical Comparison
10 Cabello, Adán
Experimental test of the free will theorem
11 Cai, Yu
Measurement-dependent locality with non-i.i.d.
measurements
12 Cavalcanti, Daniel
13 Chaves, Rafael
14 Chekhova, Maria
15 D’Ariano, Giacomo Mauro
16 De Martini, Francesco
17 De Raedt, Hans
18 DeBrota, John
19 Delsing, Per
20 Disilvestro, Leonardo
21 Dumitru, Irina Mihaela
22 Dzhafarov, Ehtibar
23 Franson, James
24 Fuchs, Christopher
Certification of quantum teleportation for all
entangled states
Experimental Test of Nonlocal Causality
Shaping the spatial spectrum of bright squeezed
vacuum in an SU(1,1) interferometer
Physics without physics
ER = EPR: Quantum entanglement and the
Einstein-Rosen bridge
Discrete-event simulation of loophole-free
Bell experiments
The Minimum Distinction Between the
Quantum and the Classical
Coupling sound to an artificial atom
University of Sydney, Australia
marcus.appleby@gmail.com
University of Valladolid, Spain
baladron@cpd.uva.es
University of Hamburg, Germany
barukcic@t-online.de
Cornell University, United States
djb16@cornell.edu
Stockholm University, Sweden
ibeng@fysik.su.se
Lund University, Sweden
fredrik.brange@teorfys.lu.se
Nagoya University, Japan
buscemi@is.nagoya-u.ac.jp
University of Seville, Spain
adan@us.es
National University of Singapore, Singapore
caiyu01@gmail.com
Institute of Photonic Sciences, Spain
dcavalcanti@gmail.com
University of Cologne, Germany
rafael.csa82@gmail.com
Max-Planck Inst. for the Science of Light,
Germany • maria.chekhova@mpl.mpg.de
University of Pavia, Italy
dariano@unipv.it
Accademia dei Lincei, Italy
francesco.demartini@uniroma1.it
University of Groningen, Netherlands
h.a.de.raedt@rug.nl
University of Massachusetts Boston, USA
jdebrota@gmail.com
Chalmers University of Technology, Sweden
per.delsing@chalmers.se
Quantum Protocols within Spekkens’ Toy Model Telecom ParisTech, France
disilves@telecom-paristech.fr
Isoentangled bases in bipartite systems
Quantum Contextuality Extended to
Arbitrary Systems of Measurements
Generalized Delta Functions, Schrodinger Cats,
and Decoherence
Something on QBism
25 Geurdes, Han
Randomness in a consistent violation of CHSH
79 Giustina, Marissa
Significant-loophole-free test of local realism
with entangled photons
26 Glancy, Scott
LTASolid Inc., USA
akhmeteli@ltasolid.com
Data analysis for ”A strong loophole-free test of
local realism” Stockholm University, Sweden
irina.dumitru@fysik.su.se
Purdue University, United States
ehtibar@purdue.edu
Univ. of Maryland at Baltimore County,
USA • jfranson@umbc.edu
University of Massachusetts Boston, USA
qbism.fuchs@gmail.com
Leiden University, the Netherlands
han.geurdes@gmail.com
University of Vienna/IQOQI Vienna,
Austria • marissa.giustina@univie.ac.at
National Inst. of Standards and Technology,
USA • sglancy@nist.gov
pgname
title
contact
27 Grangier, Philippe
Einstein, Bohr, Bell, and physical reality
28 Hanson, Ronald
From the first loophole-free Bell test to a
quantum Internet CNRS, France
philippe.grangier@u-psud.fr
29 Helland, Inge
30 Iriyama, Satoshi
31 Jaeger, Gregg
32 Jimenez Farias, Osvaldo
33 Johansson, Niklas
34 Kak, Subhash
Statistical principles and the Born rule
Entropy Change in Open Systems and Itis
Application for Photosynthesis
Randomness in Quantum Mechanics
Fully controllable high dimensional quantum
systems via the Talbot effect
Efficient Classical Simulation of the
Deutsch-Jozsa and Simon’s Algorithms
Quantum Communication and Epistemology
35 Khrennikov, Andrei
After Bell
36 Khrennikova, Polina
Application of quantum master equation for
long-term prognosis of asset-prices
37 Kofler, Johannes
38 Krizek, Gerd Christian
39 La Cour, Brian
No Fine theorem for macrorealism: Eschewing the Leggett-Garg inequality
Ockham’s razor and other heuristics in the
interpretations of quantum mechanics
Decoherence: It’s not just for quantum anymore
40 Lahti, Pekka
An Axiomatic Basis for Quantum Mechanics
41 Lapkiewicz, Radek
Quantum imaging: new developments and
old questions
42 Larsson, Jan-Åke
43 Lemjid, Achraf
44 Lopez, Carlos
Delft Univ. of Technology, the Netherlands
c.smith@tudelft.nl
University of Oslo, Norway
ingeh@math.uio.no
Tokyo University of Science, Japan
iriyama@is.noda.tus.ac.jp
Boston University, United States
jaeger@bu.edu
Institute de Ciencies Fotoniques (ICFO),
Spain • oosvaaldo@gmail.com
Linköping University, Sweden
niklas.johansson@liu.se
Oklahoma State University, USA
subhash.kak@okstate.edu
Linnaeus University, Sweden
andrei.khrennikov@lnu.se
University of Leicester, UK
pk198@le.ac.uk
Max Planck Inst. of Quantum Optics (MPQ )
Germany • johannes.kofler@mpq.mpg.de
University of Vienna, Austria
gerd.krizek@univie.ac.at
The University of Texas at Austin, USA
blacour@arlut.utexas.edu
University of Turku, Finland
pekka.lahti@utu.fi
University of Warsaw, Poland
radek.lapkiewicz@fuw.edu.pl
Loopholes in Bell inequality tests of local realism, Linköping University, Sweden
avoided in a significant-loophole-free test of
jan-ake.larsson@liu.se
Bell’s theorem with entangled photons
Functional central limit theorems and
$P(\phi)_{1}$-processes for the classical and
relativistic Nelson models
Linnaeus University, Sweden
achraf.lemjid.extern@lnu.se
Specifying nonlocality of an N-partite
quantum state via its dilation characteristics
MIEM, National Research University HSE,
Russian Federation • elena.loubenets@hse.ru,
e.loub@hotmail.com
Relativistic locality and the action reaction
principles predict de Broglie waves
UAH, Spain
carlos.lopez@uah.es
46 Luis, Alfredo
Every state is nonclassical
47 Madsen, Lars
A quantum noise limited nanoparticle and
biomolecule sensor
Universidad Complutense, Spain
alluis@ucm.es
45 Loubenets, Elena R.
48 Mardari, Ghenadie
49 Marton, Johann
50 Mattar, Alejandro
51 Michielsen, Kristel
Overcoming the EPR paradox:
How to think about quanta
Underground test of quantum mechanics –
the VIP2 experiment
Experimental multipartite entanglement and
randomness certification of the W state
in the steering scenario
Discrete event simulation of double-slit
experiments
52 Nieuwenhuizen, Theodorus M.A sub-ensemble theory of ideal quantum
measurement processes
The University of Queensland, Australia
m.lars@uq.edu.au
Open Worlds Research, USA
gmardari@gmail.com
Austrian Academy of Sciences, Austria
johann.marton@oeaw.ac.at
ICFO The Institute of Photonic Sciences,
Spain • alejandro.mattar@icfo.es
Research Centre Juelich, Germany
k.michielsen@fz-juelich.de
University of Amsterdam, Netherlands
t.m.nieuwenhuizen@uva.nl
pgname
53 Ouerdiane, Habib
54 Ozawa, Masanao
55 Padgett, Miles
56 Pelosse, Yohan
57 Perinotti, Paolo
58 Plotnitsky, Arkady
59 Polyakov, Sergey
61 Pombo, Claudia
62 Ramelow, Sven
63 Rashkovskiy, Sergey
65 Sainz, Ana Belen
66 Sánchez-Kuntz, Natalia
67 Santucci, Enrica
title
contact
Holomorphic representation of Lie group and
associated unitarizing probability measures
University of Tunis El Manar, Tunisia
habib.ouerdiane@gmail.com
Photon-sparse microscopy using Ghost-Imaging
University of Glasgow, Scotland
miles.padgett@glasgow.ac.uk
Classical Instrument Model of
Cognitive Hysteresis
Complete structural characterization of quantum University of Swansea, UK
entanglement as the realization of a self-referential yohanpelosse@googlemail.com
communication task producing free random events
Interacting quantum cellular automata
field theories
Università di Pavia, Italy
paolo.perinotti@unipv.it
Three Great Divorces of Quantum Theory:
Purdue University, USA
Reality from Realism, Probability from Causality, plotnits@purdue.edu
and Locality from Relativity
Correlation Measurements of Nonclassical States NIST, USA
with Photon-number-resolving Detectors
spoly@nist.gov
On The archetypal origins of the concept of matrixThe Netherlands
clpombo@yahoo.com
Imaging single photons in time
Quantum mechanics as a theory of the
classical field
Postquantum Steering
University of Vienna, Austria
sven.ramelow@univie.ac.at
Russian Academy of Sciences, Russia
rash@ipmnet.ru
University of Bristol, United Kingdom
absainz@gmail.com
Quantum Locality, Ring’s a Bell?: Bell’s inequality UNAM, Mexico
meets local reality and true determinism
nohaynat@gmail.com
Quantum Pattern Recognition
67 Sergioli, Giuseppe
Quantum Pattern Recognition
69 Shalm, Krister
A strong loophole-free test of Bell’s inequalities
70 Skrzypczyk, Paul
Quantum steering: Quantification and
Applications
71 Slovokhotov, Yuri
Nagoya University, Japan
ozawa@is.nagoya-u.ac.jp
Mechanics and chemistry
University of Cagliari, Italy
enrica.santucci@gmail.com
University of Cagliari, Italy
giuseppe.sergioli@gmail.com
National Inst. of Standards and Technologies,
USA • kshalm@gmail.com
University of Bristol, United Kingdom
paul.skrzypczyk@bristol.ac.uk
Moscow State University, Russian Federation
slov@phys.chem.msu.ru
73 Vaidman, Lev
The meaning of weak values
75 Watanabe, Noburo
On Complexity for Open System Dynamics
76 Weihs, Gregor
Violation of Bell’s Inequality under Strict Einstein University of Innsbruck, Austria
Locality Conditions
gregor.weihs@uibk.ac.at
77 Weinfurter, Harald
78 Wengerowsky, Sören
79 Versteegh, Marijn
80 Yau, Hou
81 Zahedi, Ramin
82 Żukowski, Marek
Tel Aviv University, Israel
vaidman@post.tau.ac.il
Tokyo University of Scienc, Japan
watanabe@is.noda.tus.ac.jp
Event-ready loophole free Bell test using heralded LMU Munich, Germany
atom-atom entanglement
h.w@lmu.de
Significant-Loophole-Free Test of Bell’s Theorem ÖAW / University of Vienna, Austria
with Entangled Photons
soeren.wengerowsky@univie.ac.at
Significant-loophole-free test of local realism
with entangled photons
KTH, Sweden
verst@kth.se
On the Logical Origin of the Laws Governing
the Fundamental Forces of Nature:
A New Axiomatic “Matrix” Approach
Hokkaido University, Japan
zahedi@let.hokudai.ac.jp
A Particle with Vibration in Time and its
Mass-Proper Time Uncertainty
FDNL Research, United States
hyau@fdnresearch.us
On Entaglement of Light and Stokes Parameters University of Gdansk, Poland
marek.zukowski@univie.ac.at
Page 1
Page 2
Number theoretic features of a SIC
Marcus Appleby, University of Sydney, marcus.appleby@gmail.com
The problem of proving, or disproving SIC existence (i.e. maximal sets
of equiangular lines in CAcl, or symmetric informationally complete positive
operator valued measures in the physics literature) in every finite dimension has
been the focus of much effort since the work of Zauner in the 1990 1s, but a
solution still eludes us. It is an unusual problem, in that we have a large number
of examples which exhibit a wealth of unexpected structure additional to the
defining feature of equiangularity. So far we have not been able to use this
additional structure to prove existence. However, it is, in its own right,
extremely interesting, and it is the subject of this talk. The structure is number
theoretic in character. It turns out that SICs, in every case that has been
checked, generate a type of number field which plays a central role in algebraic
number theory. There is a remarkable interplay between the ordinary geometric
symmetries and the number-theoretic (or Galois) symmetries. It is probably
fair to say that if SIC existence is ever proved it would be just as interesting
(perhaps even more interesting) to number theorists as it would to physicists and
design theorists. The talk will describe this side of the SIC problem. No prior
knowledge of Galois theory or number theory will be assumed.
Page 3
Page 4
Page 5
Page 6
SICS --- A GRAND QUESTION FULL OF DETAILS
Ingemar Bengtsson, Stockholm University, ibeng@fysik.su.se
Schrodinger referred to quantum mechanics a 'makeshift', because it un­
critically accepts the real number system. Recent work on SIC-POVMs (by
Appleby, Flammia, McConnell, and Yard) shows that, on the contrary, quan­
tum mechanics cares deeply about the nature of numbers. I will discuss some
special properties of some infinite series of dimensions singled out for atten­
tion by this work. The technical issue I raise - when are smaller equiangular
tight frames embedded in a SIC? - is of interest for applications to (say)
adaptive radar. The underlying argument is that nothing is more practical
than a truly foundational question. [Joint work with Irina Dumitru.]
1
Page 7
Minimal Entanglement Witness From Current Correlations in
Solid State Conductors1
Ognjen Malkoc,2 Fredrik Brange,3 and Peter Samuelsson4
Department of Physics, Lund University, Box 118, SE 221 00 Lund, Sweden
Over the past two decades, entanglement witnesses have attracted much attention for
their ability of detecting all kinds of entanglement, including local realistic ones.
Witnesses are observables whose expectation value, for at least one entangled state,
takes on a value outside the range accessible for separable states. Here we investigate
how witnesses can facilitate entanglement detection in solid state conductors, where an
unambiguous demonstration of entanglement is still lacking. More specifically, we
construct witnesses that minimize the number of measurements required to detect
entangled flying qubits. In contrast to quantum optics, our minimal witnesses are based
on current cross correlations, the natural quantity measured in mesoscopic systems.
Importantly, we find that almost all entangled pure states can be detected with just two
measurements. However, quite surprisingly, the Bell states the maximally entangled
states require at least three cross correlation measurements to be detected.
1
O. Malkoc, F. Brange, P. Samuelsson, in preparation.
ognjen.malkoc@teorfys.lu.se
3
fredrik.brange@teorfys.lu.se
4
peter.samuelsson@teorfys.lu.se
2
Page 8
Thermodynamics as Statistical Comparison Francesco Buscemi, Nagoya University, buscemi@is.nagoya‐u.ac.jp Abstract: In this talk I argue that the theory of statistical comparison ‐‐ initiated in the late 1940s by works of Blackwell and developed later by Le Cam and Torgersen, among others ‐‐ provides a nice framework to understand the statistical foundations of thermodynamics (in particular, the so‐called "thermo‐majorization" criterion) and other generalized resource theories. A major point in favor of this approach is that it can be extended to the noncommutative case, thus providing valuable insights in the fully quantum case, which is otherwise poorly understood in general. Page 9
Experimental test of the free will theorem Adán Cabello, University of Seville, adan@us.es Conway and Kochen’s free will theorem states that if experimenters have free will in the sense that their choices are not a function of the past, so must some elementary particles. The free will theorem goes beyond Bell’s theorem as it connects the two fundamental resources behind quantum technologies: contextuality (which supplies the power for quantum computation) and non‐locality (the critical resource for device‐independent secure communication). We show how the theorem can be converted into an experiment testing the violation of a Bell inequality that includes sequential measurements in one of the parties [1] and report on the first experimental observation of this violation [2]. The result of this experiment reveals that quantum non‐locality can be produced when single‐particle contextuality is combined with correlations which are not non‐local by themselves. We discuss the implications of this observation and the advantages of this approach for understanding non‐locality. [1] A. Cabello, PRL 104, 220401 (2010).
[2] B.‐H. Liu, X.‐M. Hu, J.‐S. Chen, Y.‐F. Huang, Y.‐J. Han, C.‐F. Li, G.‐C. Guo and A. Cabello,
arXiv:1603.08254.
Page 10
Page 11
Certification of quantum teleportation for all entangled states
Daniel Cavalcanti, Institute of Photonic Sciences, dcavalcanti@gmail.com
Quantum teleportation is one the cornerstones of quantum information science, serving as a
primitive in several quantum information tasks. It has become a testbed for quantum information
platforms, having been demonstrated with a variety of physical systems. The benchmark for
quantum teleportation is the average fidelity between the input and output states of the process.
According to this figure-of-merit not all entangled states can lead to the demonstration of quantum
teleportation. In this talk I will we discuss a method to certify quantum teleportation using the full
information available in a teleportation experiment and show that all entangled states are useful for
the certification of quantum teleportation. Furthermore this certification can be done reliably with
incomplete Bell state measurements or with inefficient detectors. I will also discuss the connection
of quantum teleportation to the new fundamental topics of quantum steering and Bell inequalities
with quantum inputs.
Page 12
Page 13
Shaping the spatial spectrum of bright squeezed vacuum in an SU(1,1) interferometer
Angela Pérez1,2, Lina Beltrán1,2, Timur Iskhakov3, Robert Fickler4, Samuel Lemieux4, Polina
Sharapova5,6,7, Mathieu Manceau1, Olga Tikhonova5,7, Robert Boyd4,8,9, Gerd Leuchs1,2,8, and Maria
Chekhova1,2,5
1
Max Planck Institute for the Science of Light, Guenther-Scharowsky Strasse 1, Bau 24, 91058 Erlangen,
Germany; 2Department of Physics, University of Erlangen-Nuremberg, Staudtstrasse 7/B2, 91058
Erlangen, Germany; 3Department of Physics, Technical University of Denmark, Fysikvej Building 309,
Kgs. Lyngby 2800, Denmark; 4University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5,
Canada; 5Physics Department, Lomonosov Moscow State University, Moscow 119991, Russia; 6University
of Paderborn, Paderborn, Germany; 7Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State
University, Moscow 119234, Russia; 8Max Planck Centre for Extreme and Quantum Photonics, 25
Templeton Street, Ottawa, Ontario K1N 6N5; 9Institute of Optics, University of Rochester, Rochester, New
York 14627, USA
Bright squeezed vacuum (BSV) is a macroscopic state of light featuring nonclassical properties,
from photon-number entanglement and quadrature squeezing to the violation of certain types of
Bell’s inequalities. By generating BSV through high-gain parametric down-conversion in two
subsequent coherently pumped crystals, one obtains a nonlinear SU(1,1) interferometer, which
offers various interesting possibilities. Among others, this is shaping the BSV in space/angle [1]
and time/frequency [2]. In this presentation, the focus will be on the spatial/angular spectrum and,
in particular, on obtaining BSV in optical angular momentum (OAM) modes.
We achieved generation of BSV with a variable number of spatial modes, up to the single-mode
case, by spatially separating the two crystals forming the interferometer. At some distances
between the crystals, one observes a close-to-Gaussian BSV beam, with a high degree of spatial
coherence, which indicates the presence of nearly a single spatial mode. At other distances, the
spectrum consists of a few concentric rings and contains several modes carrying OAM. By
measuring the OAM content of the beam as well as its second-order correlation function, we
demonstrate that the number of OAM modes can be changed by varying the distance between the
crystals. Using a mode sorter in such a scheme, one can measure photon-number correlations
between different OAM modes.
The obtained BSV with variable spatial properties can be used for different applications such as
conditional preparation of non-Gaussian states, quantum imaging, quantum phase measurements,
and enhanced interactions with material objects such as atoms or small particles.
[1] A. M. Pérez, T. Sh. Iskhakov, P. Sharapova, S. Lemieux, O. V. Tikhonova, M. V. Chekhova,
and G. Leuchs, Opt. Lett. 39, 2403 (2014).
[2] T. Sh. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, and M. V. Chekhova, Journal
of Modern Optics 63, 64 (2016).
Page 14
Giacomo Mauro D'Ariano
Professor of Theoretical Physics
Quantum Foundations
and Quantum Information
Dipartimento di Fisica,
via Bassi 6, I-27100 Pavia, Italy
email: dariano@unipv.it TITLE: Physics without physics
ABSTRACT: Informationalism provide a route for axiomatization of Physics thus solving the VI Hilbert
problem. Physics can be derived from “principles” stated in form of purely mathematical axioms,
without physical “primitives” (as mass, space, time), but having a thorough physical interpretation. I will
show how physical notions emerge from a theory purely mathematical axiomatized, and even how the
same standards for mass, length and time enter in the theory. As a relevant example, I will show how
the relativity principle is stated in purely mathematical terms. I will finally discuss the “a priori” nature
of principles. Page 15
ER = EPR QUANTUM ENTANGLEMENT BY THE EINSTEIN – ROSEN BRIDGE Francesco De Martini Accademia dei Lincei, Roma, Italy, francesco.demartini@uniroma1.it
___________________________________ An interesting recent theoretical speculation by Juan Maldacena and Leonard Susskind [1] considers the closed, albeit hidden, relationship existing between the content of two important works by Albert Einstein, both published in 1935. The first one [2] considers that General Relativity contains solutions in which two distant Schwarzschild black‐holes are connected through the internal coordinates via a “wormhole”: the Einstein‐Rosen bridge. These solutions can be interpreted as maximally entangled states of two black holes that form a complex EPR state [3]. It is suggested that a similar bridge might be acting within more general, simpler states, as for instance the state of two entangled spins. Then, in general: ER ‐ EPR. The theory of two entangled spins is carried out for the first time in a “complete” form, by conformal quantum geometrodynamics (CQG) i.e. by including the exact dynamics of the “internal” coordinates, the Euler angles [4]. While, the CQG dyna‐
mical theory of the space‐time “external” coordinates is found to be fully consistent with Standard Quantum Theory, the Einstein ‐ Rosen whormhole connecting the internal coordinates of the two spins is identified with the Weyl curvature scalar of the entangled system. This striking result will be discussed. _______________________ .1) J. Maldacena and L. Susskind, ArXiv: 1306‐0533v2 [hep‐th] .2) A.Einstein and N. Rosen, Phys, Rev. 48, 73 (1935). .3) A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 47, 777 (1935). .4) F. De Martini and E. Santamato, Physica Scripta, T163 014015 (2014).
Page 16
Page 17
The Minimum Distinction Between the Quantum and the Classical
John DeBrota, University of Massachusetts Boston, jdebrota@gmail.com
Recently Huangjun Zhu has filled in a missing link in the technical side of the QBism quantum foundations
program regarding rewriting all the equations of quantum theory in terms of an elegant probability formalism.
Zhu has shown that the apparatus of Symmetric Informationally Complete (SIC) quantum measurements,
previously endorsed by QBists for aesthetic reasons to do with expressing the Born Rule as an analogue to the
classical Law of Total Probability, actually defines a notion of a quasi-probability representation for quantum
states and measurements with the least amount of necessary negativity in it by a certain measure. This adds
support to the intuition that the SIC representation of quantum states makes the Born Rule appear "as
classical as possible." It furthermore gives a way of highlighting the minimal essential addition to coherence
an agent should consider when assigning probabilities. In this talk, we will explore some generalizations of
Dr. Zhu's work, including the consideration of a couple further measures of negativity, in an effort to confirm
and/or clarify the robustness of the SIC representation for these concerns. This work also has implications
for various fundamental questions in quantum computation.
1
Page 18
Coupling sound to an artificial atom M.V. Gustafsson, T. Aref, A. Frisk‐Kockum, M. Ekström, G. Johansson and P. Delsing Chalmers University of Technology, 41296 Göteborg, Sweden We present a new type of mechanical quantum device, where propagating surface acoustic wave (SAW) phonons serve as carriers for quantum information. At the core of our device is a superconducting qubit, designed to couple to SAW waves in the underlying substrate through the piezoelectric effect. This type of coupling can be very strong, and in our case exceeds the coupling to any external electromagnetic mode. The SAW waves propagate freely on the surface of the substrate, and we use a remote electro‐acoustic transducer to address the qubit acoustically. Three different experiments are presented: i) Exciting the qubit with an electromagnetic signal we can “listen” to the SAW phonons emitted by the qubit. The low speed of sound also allows us to observe the emission of the qubit in the time domain, which gives clear proof that the dominant coupling is acoustic. ii) Reflecting a SAW wave off the qubit, we observe a nonlinear reflection with strong reflection at low power and low reflection at high power. iii) Exciting the qubit with both an electromagnetic signal and with a SAW signal, we can do two tone spectroscopy on the qubit In all of these experiments we find a good agreement between experiment and theory. Future developments including giant atoms, ultrastrong coupling, and single phonon physics is also discussed. [1] M.V. Gustafsson et al., Nature Physics, 8, 338 (2012) [2] M.V. Gustafsson et al., Science 346, 207 (2014) [3] A. Frisk‐Kockum et al., Phys. Rev. A, 90, 013837 (2014) [4] T. Aref et al., arXiv:1506.01631 (2015) Page 19
Page 20
Isoentangled bases in bipartite systems
Irina Dumitru, Stockholm University, irina.dumitru@fysik.su.se
For a bipartite system of qudits H
=
Hd ® Hd, bases consisting only of
separable vectors can always be constructed, as can bases consisting of maxi­
mally entangled vectors. It is not known whether this is the case for a general
entanglement.
We investigate this question by trying to generalize Werner's construction
of maximally entangled bases. Starting from an arbitrary state, we look for d2
orthogonal vectors having the same Schmidt coefficients. Applying a method
similar to Werner's, the problem of finding a basis becomes equivalent to the
problem of reconstructing a unitary matrix from its moduli. Settling the general
question about the possibility of constructing such bases requires characterizing
the set of unistochastic matrices inside the Birkhoff polytope of bistochastic
matrices. In dimensions d :S 5, we use Latin squares to give a general answer.
1
Page 21
Page 22
Generalized Delta Functions, Schrodinger Cats, and Decoherence
J.D. Franson
University of Maryland at Baltimore County, Baltimore, MD 21250 USA
jfranson@umbc.edu
Highly nonclassical quantum states, such as a Schrödinger cat state, typically have
off-diagonal density operators while the Glauber-Sudarshan P-function corresponds
to a diagonal representation of the density operator in a basis of coherent states. Here
we investigate this situation using Dirac delta-functions with complex arguments,
which we refer to as generalized delta functions due to their unique properties. It is
shown that the generalized delta functions effectively convert diagonal elements in
the density operator into off-diagonal elements. The generalized delta functions arise
naturally in the limit of zero decoherence.
Page 23
Something on QBism
Christopher A. Fuchs
University of Massachusetts Boston, QBism.Fuchs@gmail.com
The term QBism, invented in 2009, initially stood for Quantum B ayesian­
ism, a view of quantum theory a few of us had been developing since 1993.
Eventually, however, I. J. Good's warning that there are 46,656 varieties
of Bayesianism came to bite us, with some B ayesians feeling their good
name had been hijacked. David Mermin suggested that the B in QBism
should more accurately stand for "Bruno", as in Bruno de Finetti, so that
we would at least get the variety of (subjective) Bayesianism right. The trou­
ble is QBism incorporates a kind of metaphysics that even Bruno de Finetti
might have rejected! So, trying to be as true to our story as possible, we
momentarily toyed with the idea of associating the B with what the early
20th-century United States Supreme Court Justice Oliver Wendell Holmes Jr.
called "bettabilitarianism". It is the idea that the world is loose at the joints,
that indeterminism pl ays a real role in the world. In the face of such a world,
what is an active agent to do but participate in the uncertainty that is all
around him? As Louis Menand put it, "We cannot know what consequences
the universe will attach to our choices, but we can bet on them, and we do it
every day." This is what QBism says quantum theory is about: How to best
place bets on the consequences of our actions in this quantum world. But
what an ugly, ugly word, bettabilitarianism! Therefore, maybe one should
just think of the B as standing for no word in particular, but a deep idea
instead: That the world is so wired that our actions as active agents actually
matter. Our actions and their consequences are not eliminable epiphenom­
ena. In this talk, I will describe QBism as it presently stands and give some
indication of the many things that remain to be developed.
Page 24
Randomness in a consistent violation of CHSH
Han Geurdes, Leiden university, han.geurdes@gmail.com
November 29, 2015
Abstract
A computer algorithm is demonstrated that consistently violates CHSH with
local principles. The algorithm is based on the probability loophole presented in Re­
sults in Physics, 2014,4,81-82. The basic ingredient of the algorithm is randomness.
The size of the rejection is on the average, per CHSH experiment, r::::; 0.84(1+v'2) > 2
and occurs consistently. It must be noted that the model in the cited paper has
a nonzero probability to maximally violate the CHSH. The requirement of violat­
ing 1 + v'2 is based on the obvious confusion between experimental rejection and
rejection of a basic mathematical principle. The algorithm has no " random error
of measurement". This implies that S > 2 is both necessary and sufficient support
for a nonzero probability to maximally violate the CHSH. In this way the mist of
rejection, raised in Results in Physics, 2015,5,156-157, is cleared. In the algorithm
as well as in the theoretical stress test of Results in Physics, 2014,4,81-82, one single
fixed model with random input was employed. The probability loophole is based on
a subset of non-ergodic local hidden variables models. This implies that time aver­
ages over trials need not by necessity capture all models with configuration space
averages per four CHSH setting pairs. In this sense the loophole is non-ergodic.
1
Page 25
Data analysis for "A strong loophole-free test of local realism"
Lynden K. Shalm,1 Evan Meyer-Scott,2 Bradley G. Christensen,3 Peter Bierhorst,1 Michael A. Wayne,3, 4 Martin J.
Stevens,1 Thomas Gerrits,1 Scott Glancy,1 Deny R. Hamel,5 Michael S. Allman,1 Kevin J. Coakley,1 Shellee D.
Dyer,1 Carson Hodge,1 Adriana E. Lita,1 Varun B. Verma,1 Camilla Lambrocco, 1 Edward Tortorici,1 Alan L.
Migdall,4, Y anbao Zhang,2 Daniel R. Kumor,3 William H. Farr,7 Francesco Marsili,7 Matthew D. Shaw,7
Jeffrey A. Stern,7 Carlos Abellan, 8 Waldimar Amaya,8 Valerio Pruneri,8, 9 Thomas Jennewein, 2' 1 0 Morgan W.
Mitchell,8, 9 Paul G. Kwiat, 3 Joshua C. Bienfang,4, 6 Richard P. Mirin, 1 Emanuel Knill,1 and Sae Woo Nam 1
6
1
National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
2
Institute for Quantum Computing and Department of Physics and Astronomy,
University of Waterloo, 200 University Ave West, Waterloo, Ontario, Canada, N2L 3G1
3
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
4
National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899, USA
5
Departement de Physique et d'Astronomie, Universite de Moncton, Moncton, New Brunswick ElA 3E9, Canada
6
Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland,
100 Bureau Drive, Gaithersburg, Maryland 20899, USA
7
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109
8
ICFO - Jnstitut de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, 08860 Castelldefels {Barcelona), Spain
9
!CREA - Instituci6 Catalana de Recerca i Estudis Avan9ats, 08015 Barcelona, Spain
10
Quantum Information Science Program, Canadian Institute for Advanced Research, Toronto, ON, Canada
(Dated: March 7, 2016)
Recent loophole-free tests of local realism have incorporated new analysis techniques to compute
p-values (measures of statistical significance of the experiments). The new techniques do not require
the support of assumptions upon which old techniques rely, they are effective for small data sets,
and they accommodate imperfections in random number generators used to make measurement
choices. In this talk I will describe the data analysis techniques used in the test of local realism
performed at NIST [Phys. Rev. Lett. 115, 250402]. I will review the theory used to compute
p-values, explain how it was implemented on our experiment's data, and discuss interpretation of
our p-values. [Speaking: Scott Glancy, sglancy@nist.gov]
Page 26
Einstein, Bohr, Bell, and physical reality.
Alexia Auffèves (1) and Philippe Grangier (2)
(1): Institut Néel, 25 rue des Martyrs, F38042 Grenoble, France
(2): Institut d'Optique, 2 avenue Augustin Fresnel, F91127 Palaiseau, France
Starting from the Einstein-Bohr debate, we propose a way [1] to make usual quantum
mechanics compatible with physical realism, defined as the statement that the goal of
physics is to study entities of the natural world, existing independently from any
particular observer's perception, and obeying universal and intelligible rules. Rather
than elaborating on the quantum formalism itself, we modify the quantum ontology, by
requiring that physical properties are attributed jointly to the system, and to the context
in which it is embedded. In combination with a quantization principle, this non-classical
definition of physical reality sheds new light on counter-intuitive features of quantum
mechanics such as the origin of probabilities, non-locality, and Bell’s theorem.
[1] Alexia Auffèves and Philippe Grangier, “Contexts, Systems and Modalities: a new ontology
for quantum mechanics”, Found. Phys. 46, 121 (2016); http://arxiv.org/abs/1409.2120
Page 27
Page 28
Statistical principles and the Born rule
Prof. Inge Helland
University of Oslo, ingeh@math.uio.no
The three fundamental statistical principles, the conditionality principle, the sufficiency
principle and the likelihood principle are extended to a setting corresponding to an
epistemic interpretation of quantum mechanics. Birnbaum’s theorem states that the
likelihood principle follows from the two other principles. Using this principle together
with Paul Busch’ version of Gleason’s theorem and a Dutch Book argument, we give a
proof of Born’s formula, which usually is taken as an independent axiom in quantum
mechanics.
Page 29
Page 30
Randomness in Quantum Mechanics
Prof. Gregg Jaeger, Boston University, jaeger@bu.edu
The randomness of quantum mechanics is of both of practical and fundamental
interest. In my talk, randomness is considered in relation to both. Although the
randomness of quantum theory is less distinct than is often claimed, that is, the
nature of randomness in quantum mechanics is not unrelated to the species of
randomness that have appeared in the past, its relationship to the foundations of
the theory remains profound and productive. I will argue, in particular, that
randomness is a species of unpredictability and discuss the implications of this
view for practice and for quantum foundations.
Page 31
Fully controllable high dimensional quantum systems via the Talbot effect
Osvaldo Jimenez Farias. Institute de Ciencies Fotoniques (ICFO), oosvaaldo@gmail.com
Abstract:
By means of the Talbot effect, a near field diffraction phenomenon, one can produce a discrete quantum
system of arbitrary dimension starting from a continuous variable one. More than a convenient discretization
of a continuous variable, the Talbot effect also provides the tools to manipulate and measure quantum
information. In this proposal, the free evolution of the system is a natural way of implementing unitary
operations. By adding simple phase gates, we complete a universal set of gates to manipulate the Talbot qDits [1]. We proceed by presenting the mechanism to produce pairs of maximally entangled Talbot q-Dits.
We also expose the set of measurements that render a maximal violation to Bell inequalities for nondichotomic outputs. The ideas we present here are very feasible to apply in photonic systems but this
techniques can be extended to other matter systems like Bose -Einstein condensates and atoms or molecules
in diffraction experiments [2].
[1]. O. J. Farias, et al. Quantum informationby weaving quantum Talbot Carpets. Phys. Rev. A. 91, 062328
(2015)
[2] O.J Farias et al. In preparation
Page 32
Page 33
Page 34
After Bell Andrei Khrennikov, Linnaeus University, andrei.khrennikov@lnu.se We analyze foundational consequences of recently reported loophole free tests of violation of Bell's inequality. We consider two interpretations of these remarkable experiments. The conventional one is ``Einstein was wrong and Bohr was right, there is spooky action at a distance, quantum realism is incompatible with locality.'' However, in line with discussions in literature during last decade, we show that it is still possible to treat quantum mechanics without appealing to nonlocality or denying realism. We hope that this note will call the attention of experts in quantum foundations and convince them that the case is not closed, so that they should come with their own comments on the status of the final Bell test. 1. A. Khrennikov, Contextual Approach to Quantum Formalism, Springer (2009). 2. A. Khrennikov, Beyond Quantum, Pan Stanford Publ., Singapore (2014). Page 35
Applicationofquantummasterequationforlong‐termprognosisofasset‐prices
Ms.PolinaKhrennikova,UniversityofLeicester,pk198@le.ac.uk
Abstract:Ourstudycombinesthedisciplinesofbehavioralfinanceandanextensionof
econophysics,namelytheconceptsandmathematicalstructureofquantumphysics.Weapply
theformalismofquantumtheorytomodelthedynamicsofsomecorrelatedfinancialassets,
wheretheproposedmodelcanbepotentiallyappliedfordevelopingalong‐termprognosisof
assetpriceformation.Attheinformationallevel,theassetpricestatesinteractwitheachother
bythemeansofa“financialbath”.Thelatteriscomposedofagents’expectationsaboutthe
futuredevelopmentsofassetpricesonthefinancemarket,aswellasfinanciallyimportant
informationfrommass‐media,society,andpoliticians.Oneoftheessentialbehavioralfactors
leadingtothequantum‐likedynamicsofassetpricesistheirrationalityofagents’expectations
operatingonthefinancemarket.Theseexpectationsleadtoadeepertypeofuncertainty
concerningthefuturepricedynamicsoftheassets,thangivenbyaclassicalprobabilitytheory,
e.g.,intheframeworkoftheclassicalfinancialmathematics,whichisbasedonthetheoryof
stochasticprocesses.Thequantumdimensionoftheuncertaintyinpricedynamicsis
expressedintheformoftheprice‐statessuperpositionandentanglementbetweentheprices
ofthedifferentfinancialassets.Inourmodel,theresolutionofthisdeepquantumuncertainty
ismathematicallycapturedwiththeaidofthequantummasterequation(itsquantumMarkov
approximation).Weillustrateourmodelofpreparationofafutureassetpriceprognosisbya
numericalsimulation,involvingtwocorrelatedassets.
Page 36
Page 37
Page 38
Decoherence: It's not just for quantum anymore. Brian R. La Cour Applied Research Laboratories The University of Texas at Austin Decoherence in quantum systems arises as an inevitable consequence of interactions with the environment. Theoretically, it has been used to understand the measurement problem and provide a gateway to the classical world. From a practical perspective, decoherence poses a challenge to developing large‐scale quantum computers, whose efficacy degrades with the loss of coherence. Quantum error correction meets this challenge by providing a scalable means of correcting a continuum of possible errors, as represented by a finite set of operators, using only a discrete number of components. Surprisingly, classical analog systems can exhibit similar behavior. Specifically, we demonstrate that a classical emulation of quantum gate operations, here represented by an actual analog electronic device, can be modeled accurately as a quantum operation in terms of a universal set of Pauli operators. This observation raises the possibility that quantum error correction methods may be applied to classical systems to improve fault tolerance. This work was support by the Office of Naval Research under Grant No. N00014‐14‐1‐0323. Page 39
Title:
An Axiomatic Basis for Quantum Mechanics
Pekka Lahti, University of Turku, pekka.lahti@utu.fi
Abstract: My talk is based on the paper [1] where we use the framework of
generalized probabilistic theories to present two sets of basic assumptions, called
axioms, for which we show that they lead to the Hilbert space formulation of
quantum mechanics.
[1] G. Cassinelli, P. Lahti, An Axiomatic Basis for
Quantum Mechanics, arXiv:1508.03709.
Page 40
Quantum imaging: new developments and old questions Radek Lapkiewicz Faculty of Physics, University of Warsaw I will review some of the recent advances in quantum imaging. I will address fundamental questions of the type: “Is this experiment quantum?” I will also discuss technical and application‐related issues, specifically regarding the brightness of sources used for quantum imaging and the limitations of the detection process. Page 41
Page 42
Functional central limit theorems and P( cp ) i -processes for the
classical and relativistic Nelson models
Achraf Lemjid, Linnaeus University, achraf.lemjid.extern@lnu.se
Abstract
We construct P(efi)i-processes indexed by the full time-line, separately derived from the
functional integral representations of the classical Nelson model and relativistic Nelson model in
quantum field theory. Associated with these processes we define a martingale which, under
proper scaling,
allows to obtain a central limit theorem for additive function­
als of the two processes. We show a number of examples by choosing specific functionals related
to particle-field operators.
1
Page 43
Page 44
We introduce the dilation characteristics of an N-partite quantum state that (i) quantify analytically the
maximal violation by an N-partite state of general Bell inequalities for S settings per site; (ii) trace states
admitting the S× ×S-setting LHV description; (iii) specify the numerical upper bound on the maximal Bell
violation for an N-partite state of an arbitrary Hilbert space dimension.
References
Elena R. Loubenets: On the existence of a local quasi hidden variable (LqHV) model for each N-qudit state
and the maximal quantum violation of Bell inequalities. International Journal of Quantum Information 14 (1),
1640010 [15 pp.] (2016).
Elena R. Loubenets: Context-invariant and Local Quasi Hidden Variable (qHV) Modelling Versus
Contextual and Nonlocal HV Modelling. Foundations of Physics 45, 840–850 (2015).
Elena R. Loubenets: Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann
measurements for an arbitrary Hilbert space. J. Math. Phys. 56, 032201 [21 pp.] (2015).
Elena R. Loubenets: Local quasi hidden variable (LqHV) modelling and violations of Bell-type inequalities
by a multipartite quantum state. J. Math. Phys. 53, 022201 [30 pp.] (2012).
Page 45
Page 46
A quantum noise limited nanoparticle and biomolecule sensor
Nicolas Mauranyapin1, Waleed Muhammad1, M. A. Taylor1, L. S. Madsen1, W. P. Bowen1
1.
Centre for Engineered Quantum Systems, University of Queensland, St Lucia, Queensland 4072, Australia
Email : m.lars@uq.edu.au
Biosensors that are able to detect and track single unlabelled biomolecules are an important tool both to
understand biomolecular dynamics and interactions. Recently, exceptional sensitivity has been demonstrated
using the strongly enhanced fields provided by plasmonics [1,2]. However, at high field intensities photodamage
to the biological specimen becomes increasingly problematic [3].
We demonstrate a quantum noise limited nanoparticle sensor capable of trapping and detecting the motion of
single unlabelled biomolecules such as BSA with radius as small as 3.5 nm using 104 times lower intensity
compared with state-of-the-art single molecule detectors [1,2].
Figure 1: Our approach: Nanoparticles/biomolecules get trapped in the evanescent field around an optical
nanofibre. A single trapped nanoparticle/biomolecule scatters light from a probe field into an optical nanofibre.
In the fibre the collected probe field interferes with a 70 MHz frequency shifted local oscillator field creating a
heterodyne beat note signal. The signal is thus frequency shifted away from the low frequency laser noise and
thereby the probe field can be detected at the quantum noise limit.
References
[1] Venkata R. Dantham, Stephen Holler, Curtis Barbre, David Keng, Vasily Kolchenko, and Stephen Arnold. “Label-Free
Detection of Single Protein Using a Nanoplasmonic-Photonic Hybrid Microcavity ” Nano letters (2013)
[2] Yuanjie Pang and Reuven Gordon “ Optical Trapping of a Single Protein ” Nano letters (2011)
[3] K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, “Characterization of photodamage to Escherichia
coli in optical traps,” Biophys. J. 77, 2856-2863 (1999).
Page 47
Quantum and Beyond (QB) Conference
June 13-16, 2016
Linnaeus University, Vaxjo, Sweden.
Author: Ghenadie Mardari, Open Worlds Research, gmardari@gmail.com
Title:
Overcoming the EPR paradox: How to think about quanta
Abstract: The paradoxes of quantum mechanics are purely subjective. They are caused by the improper
use of particle concepts for the analysis of wave behavior. Quantum experiments detect particles, but
they study wave properties. That is because quantum variables apply to distributions of detection
events, not to instantaneous qualities of single entities. For example, quantum superposition is not a
matter of "uncertainty" or "lack of knowledge" about the exact state of a particle. It is a matter of
certainty that all the spectral components of the wave-function apply to a quantum at the same time.
Likewise, it is natural for waves to have non-commuting variables. Yet, non-commutativity is a sufficient
condition for the violation of Bell's inequality. Hence, classical pilot-wave models reproduce the
predictions of quantum mechanics (including entangled correlations that obey Tsirelson's inequality) as
a matter of course, without non-locality. The secret to avoiding the EPR paradox is to understand that
wave-function states do not "collapse" to particle states. Instead, they evolve to acquire sharp spectra
(revealed by particle distributions). Quanta do not know how they are going to be measured. People
know where and how to place their detectors, in order to capture objective properties. The subtlety is
that waves are always in the net state of superposition. The spectrum of a net state expresses its
structure after interference, as it changes step by step, rather than a constant list of input components.
This presentation is available in full at https://youtu.be/QHStuR-Cgml.
Page 48
Underground test of quantum mechanics – the VIP2 experiment
Johann Marton
Stefan Meyer Institute Vienna (Austria)
We are experimentally investigating possible violations of standard quantum mechanics
predictions in the Gran Sasso underground laboratory in Italy. We test with high precision the
Pauli Exclusion Principle and the collapse of the wave function (collapse models).
We present our method of searching for possible small violations of the Pauli Exclusion
Principle (PEP) for electrons, through the search for "anomalous" X-ray transitions in copper
atoms, produced by "fresh" electrons (brought inside the copper bar by circulating current) which
can have the probability to undergo Pauli-forbidden transition to the 1 s level already occupied
by two electrons and we describe the VIP2 (VIolation of PEP) experiment under data taking at
the Gran Sasso underground laboratories.
In this talk the new VIP2 setup installed in the Gran Sasso underground laboratory will be
presented. The goal of VIP2 is to test the PEP for electrons with unprecedented accuracy, down
to a limit in the probability that PEP is violated at the level of 10**-31. We show preliminary
experimental results and discuss implications of a possible violation.
Page 49
Page 50
Page 51
Page 52
Page 53
Page 54
Page 55
Page 56
Interacting quantum cellular automata field theories Paolo Perinotti, paolo.perinotti@unipv.it After a short review of the derivation of free quantum field theory from quantum cellular automata, we introduce interactions as a consequence of a global gauge symmetry, and we discuss the main features of the interacting theory. We focus on one‐dimensional case, where the interacting quantum cellular automaton can be diagonalized by Bethe ansatz techniques borrowed from studies on the Hubbard model. We discuss the main features of the solution, and conclude with a perspective on the generalization to higher dimensions. Page 57
ThreeGreatDivorcesofQuantumTheory:
RealityfromRealism,ProbabilityfromCausality,andLocalityfromRelativity.
Prof.ArcadyPlotnitsky,PurdueUniversity,plotnits@purdue.edu
Thispaperconsidersthreegreatdivorces,indicatedinmytitle,ofquantumtheory,
fromquantummechanicstoquantumtheory,atleastinsomeinterpretations‐‐
realityfromrealism,probabilityfromcausality,andlocalityfromrelativity.Itisof
coursecrucial,andisindeedthemainpoint,thatreality,probability,andlocalityare
stillstrictlymaintainedbyquantumtheory.Thedivorce,orperhapsthusfar,onlya
separationbetweenlocalityandrelativityinquantumtheoryisrarelyconsidered
butisimportant,especiallyinconsideringthepossibilityoffundamentalphysics
“beyondquantum,”forexample,inparticularbeyondquantumfieldtheoryinits
currentform,forexample,isconsideringquantumgravity.Whethersucha“beyond‐
quantumtheory”willcontinuetoremaindivorcedatleastfromrealismand
causality(adivorceoflocalityfromrelativityissomewhatdifferentmatter)orwill
reconcilewithboth,asEinsteinfamouslywanted,isamatterofconjectureand,at
thisstage,ofaprobabilisticassessment,abet,onone’spart.Whatisresponsiblefor
suchabet,oratheoryofsuchabet,mayitselfmirrortheepistemologyofquantum
theoryinsofarasitmayrequireadivorcefromrealismandcausality.Localityisa
strictlyphysicalmatter,butthequestionsofrealismandcausality(andbothare
linkedinterm)extendwellbeyondphysics.
Page 58
Page 59
Page 60
Page 61
Imaging single photons in time
Sven Ramelow, University of Vienna, sven.ramelow@univie.ac.at
Photons can be used for imaging not only spatially but also in the time doma in. Such "time
lenses" [1] ca n be rea lized by a dding qua dra tic pha ses profiles to the spectrum of the
wa ve-pa cket - in fully a na logy to a norma l lens introducing a qua dra tic pha se to an
extended bea m. The role of free propa ga tion in this a na logy is ta ken over by linear
dispersion for a time lens.
Experimenta lly time lenses ca n be implemented by electro-optica l modula tion or with
parametric nonlinear optical process such as four-wave mixing (FWM). For classical fields
the la tter ena bles opera tion over multiple THz of ba ndwidth to a chieve sub-picosecond
resolution [2] enhancing the timing resolution of conventional electronic photodetectors by
orders of ma gnitude. Unfortuna tely however, this type of rea liza tion of a time lens is not
suita ble for qua ntum sta tes of light, such a s single photons, beca use of its intrinsic and
unavoidable noise from spontaneous FWM.
Here, we present the first experimental demonstration of a full time-lens suitable for single
photons. Using a ll fiber integra ted four-wa ve-mixing Bra gg Sca ttering a nd with negligible
noise [3] a nd optima l fiber dispersion we demonstra te a tempora l ma gnifica tion of > 100
for wea k pulses conta ining on a vera ge 0.05 photons. Using 90 ps jitter superconducting
detectors and our time-lens, we directly resolve a separation of two such pulses of only 2.7
ps. Using only sta nda rd fiber technology our a pproa ch ca n offer sub-200-fs resolution
single photon detection, with far reaching fundamental and technological relevance.
[1]. B. H. Koiner and M. Nazarathy, "Temporal imaging with a time lens.," Optics letters 14,630--632 (1989)
[2]. R. Salem, M.A. Foster,and A. L. Gaeta, "Application of space-time duality to ultrahigh-speed optical
signal processing," Advances in Optics and Photonics 5,274 (2013).
[3] Farsi,Alessandro,Stephane Clemmen,Sven Ramelow,and Alexander L. Gaeta. "Low-Noise Quantum
Frequency Translation of Single Photons." In CLEO: 2015,FM3A.4. 2015. doi:10.1364/CLEO_QELS.
2015.FM3A.4.
Page 62
Quantum mechanics as a theory of the classical field
Sergey A. Rashkovskiy
Institute for Problems in Mechanics of the Russian Academy of Sciences, Vernadskogo Ave.,
101/1, Moscow, 119526, Russia, E-mail: rash@ipmnet.ru, Tel. +7 906 0318854
I argue that light is a continuous classical electromagnetic wave, while the observed so-called
quantum nature of the interaction of light with matter is connected to the discrete (atomic)
structure of matter and to the specific nature of the light-atom interaction. From this point of
view, the Born rule for light is derived, and the double-slit experiment is analysed in detail. I
show that the doublesolely on the basis of classical electrodynamics. I show that within this framework, the
fundamental limitations in accuracy of the simultaneous measurement of position and
momentum or time and energy. I argue also that we can avoid the paradoxes connected with the
wave-particle duality of the electron if we consider some classical wave field - instead of electrons as the particles and consider the wave equations (Dirac, Kleinelectromagnetic field. It is shown that such an electron field must have an electric charge, an
intrinsic angular momentum and an intrinsic magnetic moment continuously distributed in the
space. It is shown that from this perspective, the doublerule, the Heisenberg uncertainty principle and the Compton effect all have a simple explanation
within classical field theory. It is shown that all of the basic properties of the hydrogen atom can
be consistently described in terms of classical electrodynamics, if instead of considering the
electron to be a particle we will consider an electrically charged classical wave field - an
- which is held by the electrostatic field of the proton In the framework of
classical electrodynamics, all of the well-known regularities of the spontaneous emission of the
hydrogen atom are obtained, which is usually derived in the framework of quantum
electrodynamics. It is shown that there are no discrete states and discrete energy levels of the
atom: the energy of the atom and its states change continuously. An explanation of the
conventional corpuscular-statistical interpretation of atomic phenomena is given. It is shown that
this explanation is only a misinterpretation of continuous deterministic processes. In the
accounts for the inverse action of self-electromagnetic radiation of the electron wave and
completely describes the spontaneous emissions of an atom. From this point of view, a lightatom interaction is considered. In particular, atom excitation by light that accounts for damping
due to spontaneous emission is fully described in the framework of classical field theory. I show
that three well-known laws of the photoelectric effect can also be derived and that all of its basic
properties can be described within classical field theory. From this point of view, a fully classical
radiation and the Einstein A-coefficient for spontaneous emission are derived in the framework
of classical field
energy density of thermal radiation is apparently not a universal function of frequency, as
law is
valid only as an approximation in the limit of weak excitation of atoms. These results show that
quantum mechanics must be considered to be not a theory of particles but a classical field theory
in the spirit of classical electrodynamics. In this case, we are not faced with difficulties in
interpreting the results of the theory.
Page 63
References
1.
2.
3.
4.
5.
6.
Rashkovskiy S.A. Quantum mechanics without quanta: the nature of the wave-particle
duality of light // Quantum Studies: Mathematics and Foundations, (Published online 31
October 2015), DOI: 10.1007/s40509-015-0063-5.
Rashkovskiy S. A. Are there photons in fact? Proc. SPIE. 9570, The Nature of Light: What
are Photons? VI, 95700G. (September 10, 2015) doi: 10.1117/12.2185010.
Rashkovskiy S.A. Semiclassical simulation of the double-slit experiments with single
photons. Progress of Theoretical and Experimental Physics, 2015 (12): 123A03 (16 pages)
DOI: 10.1093/ptep/ptv162.
Rashkovskiy S.A. Quantum mechanics without quanta. arXiv 1507.02113 [quant-ph]
(PART 2: The nature of the electron), 2016, 61p.
Rashkovskiy S.A. Classical theory of the hydrogen atom, arXiv:1602.04090 [physics.genph], 2016, 32 p.
Rashkovskiy S.A. Classical-field description of the quantum effects in the light-atom
interaction, arXiv:1603.02102 [physics.gen-ph], 2016, 28 p.
Page 64
Page 65
Page 66
Quantum Pattern Recognition
Authors' names and affiliation:
1) Giuseppe Sergioli - University of Cagliari giuseppe.sergioli@gmail.com
2) Enrica Santucci - University of Cagliari enrica.santucci@gmail.com
3) Luca Didaci - University of Cagliari didaci@diee.unica.it
4) Roberto Giuntini - University of Cagliari giuntini@unica.it
We introduce a new framework for describ ing pattern recognition tasks by
means of the mathematical language of density matrices.
In recent years, many efforts to apply the quantum formalism to non-microscopic
contexts have b een made and, in this direction, important contrib utions in the
areas of pattern recognition and image understanding have b een provided
[1,2,5,6,7]. Even if these results seem to suggest some possible computational
advantages of an approach of this sort, an extensive and universally recognized
treatment of the topic is still missing [6,4,3].
The natural motivations which have led to use quantum states for the purpose of
representing patterns are i) the possibility to exploit quantum algorithms to boost
the computational intensive parts of the classification process, ii) the possibility
of using quantum-inspired algorithms for solving classical prob lems more
effectively.
In our work, firstly we provide a one-to-one correspondence b etween patterns,
expressed as n-dimensional feature vectors (according to the standard pattern
recognition approach), and pure density operators (i.e. points in the n­
dimensional Bloch hypersphere) called "density patterns". By using this
correspondence, we give a representation of the well-known Nearest Mean
classifier (NMC) in terms of quantum objects by defining an ad hoe Normalized
Trace Distance (which coincides with the Euclidean distance b etween patterns
in the real space).
Consequently, we have found a quantum version of the discriminant function by
means of Pauli components, represented as a plane which intersects the Bloch
hypersphere.
This first result suggests future potential developments, which consist in finding
a quantum algorithm ab le to implement the normalized trace distance between
density patterns with a consequent significative reduction of the computational
complexity of the process.
But the main result we show consists in introducing a purely quantum classifier
(QC), which has not any kind of classical counterpart, through a new definition of
"Quantum Centroid". The convenience of using this Quantum Centroid lies in the
fact that it seems to be more informative than the classical one because it takes
into account also information about the distribution of the patterns.
As a consequence, the main implementative result consists in showing how this
quantum classifier performs a significative reduction of the error and an
improvement of the accuracy and precision of the algorithm with respect to the
Page 67
NMC (and also to other commonly used classifiers) on a classical computer.
The behaviors of QC and NMC on different datasets will be shown and
compared.
References:
[1] D. Aerts, B. D'Hooghe, Classical logical versus quantum conceptual thought:
examples in economics, decision theory and concept theory, Quantum
interaction, Lecture Notes in Comput. Sci., 5494:128-142, Springer, Berlin
(2009).
[2] H. Freytes, G. Sergioli, and A. Arico, Representing continuous t-norms in
quantum computation with mixed states, J. Phys. A, 43(46):465306, 12 (2010).
[3] A. Manju, M.J. Nigam, Applications of quantum inspired computational
intelligence: a survey, Artificial Intelligence Review, 42(1):79-156 (2014).
[4] C.D. Manning, P. Raghavan, and H. Schutze, Introduction to information
retrieval, Vol.1, Cambridge University Press, Cambridge (2008).
[5] M. Schuld, I. Sinayskiy, F. Petruccione, An introduction to quantum machine
learning, Contemp. Phys., 56(2), arXiv:1409.3097 (2014)
[6] H.P. Stapp, Mind, matter, and quantum mechanics, Springer-Verlag, Berlin
(1993).
[7] C. A. Trugenberger, "Quantum pattern recognition", Quantum lnf. Process,
1 (6):471-493 (2002).
Page 68
Page 69
Quantum steering: Quantification and Applications Dr. Paul Skrzypczyk, University of Bristol, paul.skrzypczyk@bristol.ac.uk In this talk I will introduce the notion of quantum (or Einstein‐Podolsky‐Rosen) steering, and presents some of its applications from a one‐sided device‐independent perspective. In particular, I will show how one can quantify quantum steering, how it can be used for randomness certification and to estimate entanglement and measurement incompatibility. Page 70
Mechanics and chemistry
Yuri L.Slovokhotov, Department of Chemistry, Moscow State University, Russia
email: slov@phys.chem.msu.ru
A direct quantum mechanical description of chemical reactions (i.e. transformations of
substances) will be suggested for several basic models of chemistry, and the consequences will
be discussed. Typical applications of quantum mechanics in chemistry (quantum chemistry) are
reductionist and indirect: redistribution of bonds between atoms is modeled in microscopic
many-particle quantum system, whereas measurable macroscopic effects (thermal data, rate of
reaction, etc.) are calculated using classical statistical thermodynamics. Meantime, many
qualitative theories of chemistry allow for a direct introduction of quantum formalism.
The very basic scheme of chemical transformation of reagents {ai} into products {bj}
a1 + a2 + a3
b1 + b2 + b3 +
(1)
usually focuses on a few key reagents and goal products ignoring a huge number of minor
components (admixtures in reagents, intermediates, by-products, etc.). A more realistic picture,
related to contemporary combinatorial chemistry, represents a reaction as a distribution of
(b1,b2 bj ) in a
reagents F(a1,a2 ai, ) transformed into distribution of products
multidimensional stoichiometry space of all compounds allowed by sorts and number of atoms in
a system. With a transforming operator R = || Rij || (1) turns into
(1a)
(b1,b2
= R F(a1,a2
,
j
i
which fits better to quantum formalism. Multi-component distributions of reagents and products
as the goal product(s) {bk} play a role of eigenvectors
thus correspond to
Ano
scheme of theoretical chemistry is a frontier orbital
concept. In a common version, it states that a result of chemical reaction (e.g. addition or
substitution at the particular atom in a substrate moiety) is guided by the wave function of
valence electrons of the substrate. Taken literally, this statement is incorrect: an attacking
fragment of sever
Nevertheless, frontier orbital schemes work well in
prediction of reaction paths. In fact, these schemes indirectly suggest that distributions
attacking particles near a substrate correspond to wave functions. Substitution of hydrogen atoms
for chlorine in paraffine hydrocarbons CnH2n+2 will be discussed in more detail [1].
In physical chemistry, transformation of reagents to
products is usually represented by movement of a point
along reaction profile over a potential barrier. Classical
movement of the point, forced by thermal energy, reflects
E0
the energetic effect of reaction H=EA EB and exponential
dependence k~exp( E0/RT) of the rate constant k on inverse
temperature (Figure 1). If the moving point is a quantum
particle, the model immediately gives such fundamental
chemical phenomena as reverse reaction and chemical
Figure 1
equilibrium at any temperature (reflection of a quantum
particle), and the existence of unstable intermediates (quasi-bound states above barrier) together
with negative exponential probability of a particle with E<E0 to penetrate a barrier (quantum
Page 71
px
tunneling). Many theoretical models of chemistry are particularly suitable for quantization ,
which may point to inherently quantum nature of chemical phenomena.
A lot of quantum-like models in modern economic and social sciences [2] (as well as in
chemistry) draw to fundamental problems of mechanics per se, including the possibility of
mechanical modeling of real world. The grounds of
(as noted in many textbooks) due to some logical misfit in
ncorporates the essentially
their postulates. We believe
classical principle: a precise correspondence of theoretical model to physical reality. This
principle, absent in Bohmian mechanics, demands a literal imaging of individual quantum
system (instead of ensemble) by a quantum model, creating misunderstanding and paradoxes.
A big advantage of Bohmian mechanics is a possibility to use fractal trajectories in
description of a quantum system
It permits a system to be at particular trajectory
point at any moment of time without precise fixing its point in a next moment. The
(convergent in probability) derivatives of a fractal function allow for simultaneous measurements
of conjugate variables (proven in experiments with atomic
beams [3]). Fractal trajectories are experimentally observed,
e.g. as time series of financial data. Fractal phase trajectories,
whose outlier points are intermixed, help to understand interstate transitions in a quantum system (Figure 2). Since all
experimentally registered trajectories, as sets of points, are
essentially fractal, re-determination of the place of quantum
mechanics (and, generally, of mechanics in its quantum and
x
relativistic version) in modeling physical world, is needed.
Figure 2
Basing on various, partially conflicting sources, we may characterize mechanics as
mathematical modeling with the restrictions posed by most fundamental properties of Nature
(position, velocity, inertia, potentials and forces). Taken mechanics, as a framework of a physical
theory, in its general quantum and relativistic version, we arrive to a theorem.
Any phenomenon of the real world may be approximated by a mechanical model that
reproduces one, or several, of its measurable parameters at any pre-determined accuracy level.
Application of mechani
all
observed phenomena allows to circumvent a bunch of quasi-philosophical problems of scale (in
dimensions, velocities, etc.) that a system must fit for its quantum or relativistic modeling to be
correct. In fact, most quasy-mechanical theories in economics, control science, or finance, are
assumed to use classical mechanics, whereas from our viewpoint, a particular classical character
of such models has to be proven. This sort of a generalized mechanistic theory may provide new
insight into unusual features of human-made objects (e.g. networks) and their dynamics.
References
1. Y.L.Slovokhotov. Quantum mechanics from chemical viewpoint. Rossijskij khimicheskij
zhurnal (Russian Chemical Jourmal), 1998, v. 42 N3, p.p. 5 17 (in Russian).
2. A.Khrennikov. Ubiquitous Quantum Structure: From Psychology to Finance. Berlin;
Heidelberg; New York, NY: Springer (2010).
3. C.H.Kurtsiefer, T.Pfau, J.Mlynek, Measurement of the Wigner function of an ensemble of
helium atoms, Nature. 1997, v. 386, p.p. 150-153.
Page 72
Page 73
Page 74
Page 75
Violation of Bell’s Inequality under Strict
Einstein Locality Conditions
Gregor Weihs, University of Innsbruck, gregor.weihs@uibk.ac.at
In 2015 three experiments finally achieved demonstrations of quantum mechanical correlations that
refute local realistic hidden variable models as envisioned by Einstein and Bell without any obvious
shortcomings. From the start in the 1970s by Clauser and others new technology had to be
developed for every step of improvement. Sources, analyzers, randomizers, and detectors of the
highest grade were required to close all the loopholes.
In the mid-1990s armed with a newly developed source of entangled photon pairs we set out to close
the so-called locality loophole by ensuring for the first time that the entire measurement on one side
of the apparatus including randomly setting the analyzers happened outside the backward lightcone
of the other side’s measurement. In addition all data recording was done locally. Several ideas
developed in this experiment [1] have become standard practice in Bell-inequality experiments since.
[1] G. Weihs, T. Jennewein, C. Simon, H. Weinfurter and A. Zeilinger, Violation of Bell’s inequality
under strict Einstein locality conditions, Physical Review Letters 81 (21), 5039–5043 (1998).
DOI: 10.1103/PhysRevLett.81.5039
Page 76
Event-ready loophole free Bell test
using heralded atom-atom entanglement
Wenjamin Rosenfeld, Daniel Burchardt, Robert Garthoff,
Michael Krug, Norbert Ortegel, Kai Redeker,
and Harald Weinfurter
Fakultät für Physik, Ludwig-Maximilians-Universität, D-80797 München, Germany
Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
Atom-photon entanglement together with entanglement swapping
enables an event-ready Bell experiment closing the detection as well
as the locality loophole.
Atomic states offer clear advantages for Bell experiments due to the high detection
efficiency. In our experiment two entangled atom-photon couples separated by 400 m
line of sight are combined using entanglement swapping. In spite of comparatively low
collection efficiency of the photons, we obtain about 1-2 entangled atom pairs per
minute. The Bell-state measurement of the entanglement swapping protocol,
implemented to detect both
and
, heralds each measurement run. It serves
as signal for the observers to start their measurements and to report on their respective
results for every run. In this case a limited detection efficiency is not an issue anymore
and enters only in the noise of the experiment. Thus the well-known
Clauser-Horn-Shimony-Holt (CHSH) Bell-inequality can be used to obtain reasonable
significance with a modest number of events.
Warranting space-like separated observation of the state of the two atoms is
enabled by introducing a state dependent ionisation scheme with detection efficiency
of the fragments above 95% within less than 800 ns. The random number generation is
achieved by sampling a telegraph signal and, without any post-processing, exhibits no
bias. No correlations are observable for times longer than 100 ns, which altogether
makes the two observers truly independent from each other.
A CHSH S-parameter of
corresponding to detection of
(
afer detection of
) was obtained after observing 325 events
within 6.4 hours clearly violating local realistic predictions.
Page 77
Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons
Sören Wengerowsky, ÖAW / University of Vienna,
soeren.wengerowsky@univie.ac.at
Local realism is the worldview in which physical properties of objects exist independently of
measurement and where physical influences cannot travel faster than the speed of light. Bell’s theorem
states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in
Bell’s inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every
experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report
a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized
source of entangled photons, rapid setting generation, and highly efficient superconducting detectors,
we observe a violation of a Bell inequality with high statistical significance. The purely statistical
−31
probability of our results to occur under local realism does not exceed 3.74 x 10
11.5 standard deviation effect.
Page 78
, corresponding to an
SIGNIFICANT-LOOPHOLE-FREE TEST OF LOCAL REALISM
WITH ENTANGLED PHOTONS
Marissa Giustina1,2,a, Marijn A. M. Versteegh1,2,3,b, Sören Wengerowsky1,2,c, Johannes
Handsteiner1,2,d, Armin Hochrainer1,2,e, Kevin Phelan1,f, Fabian Steinlechner1,g,
Johannes Kofler4,h, Jan-Åke Larsson5,i, Carlos Abellán6,7,j, Waldimar Amaya6,7,k,
Valerio Pruneri6,7,l, Morgan W. Mitchell6,7,m, Jörn Beyer8,n, Thomas Gerrits9,o,
Adriana E. Lita9,p, Lynden K. Shalm9,q, Sae Woo Nam9,r, Thomas Scheidl1,2,s, Rupert
Ursin1,2,t, Bernhard Wittmann1,2,u, Anton Zeilinger1,2,v
1
IQOQI, Austrian Academy of Sciences, Vienna, Austria
2
Faculty of Physics, University of Vienna, Vienna, Austria
3
Department of Applied Physics, KTH, Stockholm, Sweden
4
Max-Planck-Institute of Quantum Optics, Garching, Germany
5
Institutionen för Systemteknik, Linköpings Universitet, Linköping, Sweden
6
ICFO, Barcelona, Spain
7
ICREA, Barcelona, Spain
8
Physikalisch-Technische Bundesanstalt, Berlin, Germany
9
NIST, Boulder, Colorado, USA
Local realism is the worldview in which physical properties of objects exist independently
of measurement and where physical influences cannot travel faster than the speed of light.
Bell’s theorem states that this worldview is incompatible with the predictions of quantum
mechanics, as is expressed in Bell’s inequalities. Previous experiments convincingly
supported the quantum predictions. Yet, every experiment requires assumptions that
provide loopholes for a local realist explanation. Here, we report a Bell test that closes the
most significant of these loopholes simultaneously. Using a well-optimized source of
entangled photons, rapid setting generation, and highly efficient superconducting detectors,
we observe a violation of a Bell inequality with high statistical significance. The purely
statistical probability of our results to occur under local realism does not exceed 3.74 ×
10−31, corresponding to an 11.5 standard deviation effect.
Reference:
[1] “Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons”, M.
Giustina et al., Phys. Rev. Lett. 115, 250401 (2015).
a) marissa.giustina@univie.ac.at; b) verst@kth.se; c) soeren.wengerowsky@univie.ac.at;
d) johannes.handsteiner@univie.ac.at; e) armin.hochrainer@univie.ac.at; f) kevinphe@googlemail.com;
g) fabian-oliver.steinlechner@univie.ac.at; h) johannes.kofler@univie.ac.at; i) jan-ake.larsson@liu.se;
j) carlos.abellan@icfo.es; k) wladimar.amaya@icfo.es; l) valerio.pruneri@icfo.es;
m) morgan.mitchell@icfo.es; n) joern.beyer@ptb.de; o) gerrits@boulder.nist.gov; p) adriana.lita@nist.gov;
q) lynden.shalm@nist.gov; r) saewoo.nam@nist.gov; s) thomas.scheidl@univie.ac.at;
t) rupert.ursin@univie.ac.at; u) bernhard.wittmann@univie.ac.at; v) anton.zeilinger@univie.ac.at.
Page 79
Hou Yau
FDNL Research, USA
hyau@fdnresearch.us
A Particle with Oscillation in Time and its Mass-Proper Time Uncertainty
We study the quantum properties of a particle that has oscillation in time. Treating time as a dynamical
variable, we first construct a wave with 4-vector amplitude that has matters vibrating in space and
time. By analyzing its Hamiltonian density equation, we find that such system shall be treated as a
quantized field. This quantized real scalar field obeys the Klein-Gordon equation and has properties
resemble a zero spin bosonic field. In addition, the particle observed has oscillation in proper time. As a
simple harmonic oscillator, the energy of this particle is always positive. Here, we use these properties
to establish an uncertainty relation between the mass-energy and proper time of the particle. Time in
this system can be treated as a self-adjoint operator.
Page 80
On the Logical Origin of the Laws Governing the Fundamental Forces of
Nature: A New Axiomatic “Matrix” Approach
Ramin Zahedi1
1
Logic and Philosophy of Science Research Group, Hokkaido University, Japan. Email: zahedi@let.hokudai.ac.jp
Moreover, based on the unique structure of general
relativistic particle wave equations derived and also
the assumption of chiral symmetry as a basic discrete
symmetry of the source-free cases of these fields, it
has been proven that the universe cannot have more
than four space-time dimensions. In addition, an
argument for the asymmetry of left and right handed
(interacting) particles is presented. Furthermore, on
the basis of definite mathematical structure of the
field equations derived, it is also shown that magnetic
monopoles (in contrast with electric monopoles)
could not exist in nature.
Abstract: This article is an expanded version of my
previous publication Ref. [1], 2015. In part I of
this article, I provide an analysis and overview
concerning discrete physics. In Part II (the main part)
of this article I present a new axiomatic matrix
approach based on the ring theory (including the
integral domains) and the generalized Clifford
algebra. On the basis of this (primary) mathematical
approach, by linearization (and simultaneous
parameterization, as necessary algebraic conditions),
followed by first quantization of the relativistic
energy-momentum relation (defined algebraically for
a single particle with invariant mass m_0), a unique
and original set of the general relativistic (singleparticle) wave equations are derived directly.
These equations are shown to correspond uniquely to
certain massive forms of the laws governing the
fundamental forces of nature, including the
Gravitational (Einstein), Electromagnetic (Maxwell)
and Nuclear (Yang-Mills) field equations (formulated
solely in (1+3) dimensional space-time), in addition
to the (half-integer spin) single-particle wave
equations such as the Dirac equation (which are
formulated solely in (1+2) dimensional space-time).
In particular, a unique massive form of the general
theory of relativity – with a definite complex
torsion – is shown to be obtained solely by first
quantization of a special relativistic algebraic matrix
relation. In addition, it is shown that the "massive"
Lagrangian density of the obtained Maxwell and
Yang-Mills fields could be also locally gauge
invariant – where these fields are formally represented on a background space-time with certain
complex torsion which is generated by the invariant
mass of the gauge field carrier particle. Subsequently,
in agreement with certain experimental data, the
invariant mass of a particle (that actually would be
identified as massive photon) has been specified
(m_γ ≈ 1.4774231 ×10 ^-41 kg), which is coupled to
background space-time geometry.
References
[1]- Ramin Zahedi, “On Discrete Physics: a Perfect
Deterministic Structure for Reality – And "A (Direct)
Logical Derivation of the Laws Governing the
Fundamental Forces of Nature"”, AFSIL, Hokkaido
University Publs., JAPAN, 16 (2): 1-97, 2015;
(http://eprints.lib.hokudai.ac.jp/dspace/handle/2115/6
0272 , https://INSPIREHEP.net/record/1387680).
Acknowledgment
Special thanks are extended to Prof. and
Academician Vitaly L. Ginzburg (Russia), Prof. and
Academician Dmitry V. Shirkov (Russia), Prof.
Leonid A . Shelepin (Russia), Prof. Vladimir Ya.
Fainberg (Russia), Prof. Wolfgang Rindler (USA),
Prof. Roman W. Jackiw (USA), Prof. Roger Penrose
(UK), Prof. Steven Weinberg (USA), Prof. Ezra T.
Newman (USA), Prof. Graham Jameson (UK), Prof.
Sergey A. Reshetnjak (Russia), Prof. Sir Michael
Atiyah (UK) (who, in particular, kindly encouraged
me to continue this work as a new unorthodox
(primary) mathematical approach to fundamental
physics), and many others for their support and
valuable guidance during my studies and research.
Page 81
Page 82