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Quantum Information and Communication: From Foundations to Applications

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A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (20 February 2016) | Viewed by 85924

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Prof. Dr. Gregg Jaeger

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Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA 02215, USA
Interests: quantum information; foundations of quantum mechanics; quantum cryptography; quantum metrology; history and philosophy of science; quantum optics; stochastic processes; genetics
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Prof. Dr. Andrei Khrennikov

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International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden
Interests: quantum foundations; information; probability; contextuality; applications of the mathematical formalism of quantum theory outside of physics: cognition, psychology, decision making, economics, finances, and social and political sciences; p-adic numbers; p-adic and ultrametric analysis; dynamical systems; p-adic theoretical physics; utrametric models of cognition and psychological behavior; p-adic models in geophysics and petroleum research
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Special Issue Information

Dear Colleagues,

Recent years have been characterized by a tremendous development of quantum information and communication, both in theory and experiment: quantum computers and, recently, quantum stimulators, cryptography, teleportation, and quantum random generators. It is now clear that this great project is essentially more complex than one would have expected at its initial stage and that its realization demands much more effort on the parts of both theoreticians and experimenters. This is a good time to examine and summarize the results, thus far, of various intensive studies and experimentations regarding, both, successes and difficulties. It is the moment to present expectations of the further developments of the field, to formulate further challenges and problems, and to point out any possible, hidden pitfalls for the future.

The quantum information revolution has significantly increased the interest in the foundations of quantum mechanics. This topic is no longer the business of only philosophers and historians of science, but it is now also largely unavoidable to practicing physicists, theoreticians, and even experimenters. While complemented by the more traditional philosophical analysis, foundational studies are now based, much more firmly, on complex theoretical models, advanced mathematics, and numerical simulations that are very closely related to experiments. The intensive development of quantum information and quantum technologies continually generates novel foundational problems. The problem of distinguishing classical and quantum randomness and justification of the use of quantum random generators, which before was merely a philosophic problem, plays a fundamental role in development of quantum technologies, is one example.

Recently, the mathematical formalism of quantum information theory and quantum probability has provided numerous applications outside of physics, in cognitive and social sciences, psychology, decision-making, economics, psychology, finances, and politics. In such applications, quantum theory is treated operationally as representing contextual probabilistic behavior of systems of any kind. There are plenty of statistical data, collected in the aforementioned domains of science that do not match the laws of classical probability theory (Kolmogorov, 1933), but can be successfully described and modeled in the framework of quantum theory. Such an approach in the use of quantum formalism is certainly quantum-like, even if a system itself need not necessarily be described by quantum physics; it only exhibits some non-classical information-probabilistic features, and has been exhibited in recent decades, in some situations in quantum optics, which were initially thought to absolutely require quantum entanglement, but were understandable in the absence of it as well, with quantum mechanical formalism being the preferred formal framework in any case.

The aim of this Special Issue is to encourage scientists to present original and recent developments, as well as review papers, on quantum information and communications and the related problems of quantum foundations. Quantum information is treated widely enough to even cover applications of its formalism outside of the physics mentioned above.

One of the objectives of this issue is to promote cross-fertilization among scientists working in a wide range of areas of quantum information, communication and foundations, and theory and applications; for example, interrelation of quantum information theory and theory of open quantum systems, Bell’s inequality, its probabilistic structure and especially its role in theory of quantum random generators, statistical analysis of experimental data, foundations of quantum mechanics, entanglement, and quantum-like models in decision making. One question of especially high interest (in the light of recent experiments in labs of A. Zeilinger and P. Kwiat to close the detection efficiency loophole) is the analysis of the trade-off between entanglement and non-purity of states, leading to violations of the Eberhard and Clauser-Horne versions of Bell’s inequality.

Prof. Gregg Jaeger
Prof. Andrei Khrennikov
Guest Editors

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Keywords

quantum information and communication
quantum algorithms and cryptographic protocols
quantum and classical probability
quantum and classical randomness and random generators
entanglement and its measures
trade between entanglement and non-purity
open quantum systems
quantum Markov and non-Markov dynamics
theory of quantum apparatuses and instruments
contextuality
Bell-type inequalities
statistical analysis of data
quantum-like models of cognition and decision making, in economics, psychology, finances, politics

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Published Papers (11 papers)

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27178 KiB

Open AccessArticle

Discrete Time Dirac Quantum Walk in 3+1 Dimensions

by Giacomo Mauro D’Ariano, Nicola Mosco, Paolo Perinotti and Alessandro Tosini

Entropy 2016, 18(6), 228; https://doi.org/10.3390/e18060228 - 14 Jun 2016

Cited by 7 | Viewed by 5590

Abstract

In this paper we consider quantum walks whose evolution converges to the Dirac equation in the limit of small wave-vectors. We show exact Fast Fourier implementation of the Dirac quantum walks in one, two, and three space dimensions. The behaviour of particle states—defined as states smoothly peaked in some wave-vector eigenstate of the walk—is described by an approximated dispersive differential equation that for small wave-vectors gives the usual Dirac particle and antiparticle kinematics. The accuracy of the approximation is provided in terms of a lower bound on the fidelity between the exactly evolved state and the approximated one. The jittering of the position operator expectation value for states having both a particle and an antiparticle component is analytically derived and observed in the numerical implementations. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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351 KiB

Open AccessArticle

Quantum Errors and Disturbances: Response to Busch, Lahti and Werner

by David Marcus Appleby

Entropy 2016, 18(5), 174; https://doi.org/10.3390/e18050174 - 6 May 2016

Cited by 8 | Viewed by 6183

Abstract

Busch, Lahti and Werner (BLW) have recently criticized the operator approach to the description of quantum errors and disturbances. Their criticisms are justified to the extent that the physical meaning of the operator definitions has not hitherto been adequately explained. We rectify that omission. We then examine BLW’s criticisms in the light of our analysis. We argue that, although the BLW approach favour (based on the Wasserstein two-deviation) has its uses, there are important physical situations where an operator approach is preferable. We also discuss the reason why the error-disturbance relation is still giving rise to controversies almost a century after Heisenberg first stated his microscope argument. We argue that the source of the difficulties is the problem of interpretation, which is not so wholly disconnected from experimental practicalities as is sometimes supposed. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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263 KiB

Open AccessArticle

Orthogonal Vector Computations

by Karl Svozil

Entropy 2016, 18(5), 156; https://doi.org/10.3390/e18050156 - 29 Apr 2016

Cited by 4 | Viewed by 6303

Abstract

Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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2378 KiB

Open AccessArticle

Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network

by Yoshitaka Haribara, Shoko Utsunomiya and Yoshihisa Yamamoto

Entropy 2016, 18(4), 151; https://doi.org/10.3390/e18040151 - 19 Apr 2016

Cited by 43 | Viewed by 15722

Abstract

We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential [...] Read more.

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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819 KiB

Open AccessArticle

Interference Energy Spectrum of the Infinite Square Well

by Mordecai Waegell, Yakir Aharonov and Taylor Lee Patti

Entropy 2016, 18(4), 149; https://doi.org/10.3390/e18040149 - 19 Apr 2016

Cited by 1 | Viewed by 8095

Abstract

Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction

Ψ (x, t)

with N known zeros located at points

s_{i} = (x_{i}, t_{i})

. Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The interpretation of this result with respect to the conservation of energy and the energy-time uncertainty relation is discussed, and the idea of alternate energy eigenbases is fleshed out. The question of whether or not a preferred discrete energy spectrum is an inherent feature of a particle’s quantum state is examined. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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1097 KiB

Open AccessArticle

A Quantum Query Expansion Approach for Session Search

by Peng Zhang, Jingfei Li, Benyou Wang, Xiaozhao Zhao, Dawei Song, Yuexian Hou and Massimo Melucci

Entropy 2016, 18(4), 146; https://doi.org/10.3390/e18040146 - 18 Apr 2016

Cited by 17 | Viewed by 6194

Abstract

Recently, Quantum Theory (QT) has been employed to advance the theory of Information Retrieval (IR). Various analogies between QT and IR have been established. Among them, a typical one is applying the idea of photon polarization in IR tasks, e.g., for document ranking and query expansion. In this paper, we aim to further extend this work by constructing a new superposed state of each document in the information need space, based on which we can incorporate the quantum interference idea in query expansion. We then apply the new quantum query expansion model to session search, which is a typical Web search task. Empirical evaluation on the large-scale Clueweb12 dataset has shown that the proposed model is effective in the session search tasks, demonstrating the potential of developing novel and effective IR models based on intuitions and formalisms of QT. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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863 KiB

Open AccessArticle

Exploration of Quantum Interference in Document Relevance Judgement Discrepancy

by Benyou Wang, Peng Zhang, Jingfei Li, Dawei Song, Yuexian Hou and Zhenguo Shang

Entropy 2016, 18(4), 144; https://doi.org/10.3390/e18040144 - 18 Apr 2016

Cited by 34 | Viewed by 7394

Abstract

Quantum theory has been applied in a number of fields outside physics, e.g., cognitive science and information retrieval (IR). Recently, it has been shown that quantum theory can subsume various key IR models into a single mathematical formalism of Hilbert vector spaces. While a series of quantum-inspired IR models has been proposed, limited effort has been devoted to verify the existence of the quantum-like phenomenon in real users’ information retrieval processes, from a real user study perspective. In this paper, we aim to explore and model the quantum interference in users’ relevance judgement about documents, caused by the presentation order of documents. A user study in the context of IR tasks have been carried out. The existence of the quantum interference is tested by the violation of the law of total probability and the validity of the order effect. Our main findings are: (1) there is an apparent judging discrepancy across different users and document presentation orders, and empirical data have violated the law of total probability; (2) most search trials recorded in the user study show the existence of the order effect, and the incompatible decision perspectives in the quantum question (QQ) model are valid in some trials. We further explain the judgement discrepancy in more depth, in terms of four effects (comparison, unfamiliarity, attraction and repulsion) and also analyse the dynamics of document relevance judgement in terms of the evolution of the information need subspace. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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291 KiB

Open AccessArticle

On the Stability of Classical Orbits of the Hydrogen Ground State in Stochastic Electrodynamics

by Theodorus M. Nieuwenhuizen

Entropy 2016, 18(4), 135; https://doi.org/10.3390/e18040135 - 13 Apr 2016

Cited by 11 | Viewed by 4422

Abstract

De la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics connect to a stable situation, where the electron neither collapses onto the nucleus nor gets expelled from the atom. Although the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Peña-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an

1 / r^{2}

potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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288 KiB

Open AccessArticle

Disentangling the Quantum World

by Huw Price and Ken Wharton

Entropy 2015, 17(11), 7752-7767; https://doi.org/10.3390/e17117752 - 16 Nov 2015

Cited by 43 | Viewed by 10496

Abstract

Correlations related to quantum entanglement have convinced many physicists that there must be some at-a-distance connection between separated events, at the quantum level. In the late 1940s, however, O. Costa de Beauregard proposed that such correlations can be explained without action at a distance, so long as the influence takes a zigzag path, via the intersecting past lightcones of the events in question. Costa de Beauregard’s proposal is related to what has come to be called the retrocausal loophole in Bell’s Theorem, but—like that loophole—it receives little attention, and remains poorly understood. Here we propose a new way to explain and motivate the idea. We exploit some simple symmetries to show how Costa de Beauregard’s zigzag needs to work, to explain the correlations at the core of Bell’s Theorem. As a bonus, the explanation shows how entanglement might be a much simpler matter than the orthodox view assumes—not a puzzling feature of quantum reality itself, but an entirely unpuzzling feature of our knowledge of reality, once zigzags are in play. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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Review

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890 KiB

Open AccessReview

Entropy? Honest!

by Tommaso Toffoli

Entropy 2016, 18(7), 247; https://doi.org/10.3390/e18070247 - 30 Jun 2016

Cited by 7 | Viewed by 8619

Abstract

Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons) is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable) generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1) the system’s internal dynamics; (2) unsolicited external influences on it; and (3) the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems! Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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423 KiB

Open AccessConcept Paper

Towards Information Lasers

by Andrei Khrennikov

Entropy 2015, 17(10), 6969-6994; https://doi.org/10.3390/e17106969 - 16 Oct 2015

Cited by 28 | Viewed by 5329

Abstract

Recently, the methods of quantum theory (QT), especially quantum information and probability, started to be widely applied outside of physics: in cognitive, social and political sciences, psychology, economics, finances, decision making, molecular biology and genetics. Such models can be called quantum-like, in contrast to real quantum physical cognitive and biological models. Quantum-like means that only the information and probability structures of QT are explored. This approach matches the information interpretation of QT well (e.g., Zeilinger and Brukner, Fuchs and Mermin, D’Ariano), as well as the informational viewpoint on physics in general (e.g., Wheeler’s “it from bit” paradigm). In this paper, we propose a quantum-like model of an information laser by precessing the assumptions on the structure of state spaces of information processors, “information atoms” (i-atoms) and information fields. The basic assumption is the discrete structure of state spaces related to quantization of an information analog of energy. To analyze a possible structure of the state space of i-atoms leading to the possibility to create information lasers, we have to develop a purely information version of quantum thermodynamics. We did this by placing the main attention on the derivation of the conditions for the equilibrium of information exchange between i-atoms and a quantized information field. Full article

(This article belongs to the Special Issue Quantum Information and Communication: From Foundations to Applications)

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