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Special Issue "Quantum Nonlocality"

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

Deadline for manuscript submissions: 15 December 2018

Special Issue Editor

Guest Editor
Prof. Dr. Lev Vaidman

Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
Website | E-Mail
Interests: foundations of quantum mechanics; quantum measurements; quantum cryptography; quantum communication; quantum stoppers; teleportation: methods and applications

Special Issue Information

Dear Colleagues,

Quantum mechanics was arguably the biggest revolution in the history of physics. It can be compared only with the theory of relativity. The tension between the two theories lies in the concept of (non)locality. Half a century ago, there was a second quantum revolution when the Aharonov-Bohm effect and Bell inequalities provided manifestations of nonlocality in our quantum world.

According to my understanding, the core of both of these nonlocality features is quantum entanglement. Entanglement is also the core for an objective definition of entropy. If we know the complete classical state of a system, then its entropy is zero. It is also zero when we know the complete state of a quantum system. Thus, entropy, as it relates to information, characterizes the subjective property of the lack of complete information. However, the complete description of a subsystem entangled with another does provide an objective concept of entropy for that subsystem. Entanglement provides the certificate of randomness required for an objective definition of entropy.

Although countless papers have been written on quantum nonlocality, there are still many open questions: Can quantum mechanics be derived based on nonlocality? Is there nonlocality beyond entanglement, such as collapse or the physical meaning of potentials? Have recent "loop-hole free" tests answered all experimental questions? In this Special Issue on quantum nonlocality, I invite papers answering these and other burning questions concerning quantum nonlocality. Additionally, even more welcomed are papers asking new questions in this field.

Prof. Dr. Lev Vaidman
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • action at a distance
  • entanglement
  • collapse of the quantum state
  • certification of quantum randomness
  • Aharonov-Bohm effect
  • quantum nonlocality
  • Bell inequalities

Published Papers (8 papers)

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Research

Open AccessFeature PaperArticle Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
Entropy 2018, 20(10), 763; https://doi.org/10.3390/e20100763
Received: 23 August 2018 / Revised: 19 September 2018 / Accepted: 20 September 2018 / Published: 5 October 2018
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Abstract
The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we
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The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states. Full article
(This article belongs to the Special Issue Quantum Nonlocality)
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Open AccessArticle Microscopic Theory of Energy Dissipation and Decoherence in Solid-State Quantum Devices: Need for Nonlocal Scattering Models
Entropy 2018, 20(10), 726; https://doi.org/10.3390/e20100726
Received: 24 July 2018 / Revised: 7 September 2018 / Accepted: 12 September 2018 / Published: 21 September 2018
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Abstract
Energy dissipation and decoherence in state-of-the-art quantum nanomaterials and related nanodevices are routinely described and simulated via local scattering models, namely relaxation-time and Boltzmann-like schemes. The incorporation of such local scattering approaches within the Wigner-function formalism may lead to anomalous results, such as
[...] Read more.
Energy dissipation and decoherence in state-of-the-art quantum nanomaterials and related nanodevices are routinely described and simulated via local scattering models, namely relaxation-time and Boltzmann-like schemes. The incorporation of such local scattering approaches within the Wigner-function formalism may lead to anomalous results, such as suppression of intersubband relaxation, incorrect thermalization dynamics, and violation of probability-density positivity. The primary goal of this article is to investigate a recently proposed quantum-mechanical (nonlocal) generalization (Phys. Rev. B 2017, 96, 115420) of semiclassical (local) scattering models, extending such treatment to carrier–carrier interaction, and focusing in particular on the nonlocal character of Pauli-blocking contributions. In order to concretely show the intrinsic limitations of local scattering models, a few simulated experiments of energy dissipation and decoherence in a prototypical quantum-well semiconductor nanostructure are also presented. Full article
(This article belongs to the Special Issue Quantum Nonlocality)
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Open AccessArticle Non-Local Parity Measurements and the Quantum Pigeonhole Effect
Entropy 2018, 20(8), 606; https://doi.org/10.3390/e20080606
Received: 5 June 2018 / Revised: 6 August 2018 / Accepted: 8 August 2018 / Published: 16 August 2018
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Abstract
The pigeonhole principle upholds the idea that by ascribing to three different particles either one of two properties, we necessarily end up in a situation when at least two of the particles have the same property. In quantum physics, this principle is violated
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The pigeonhole principle upholds the idea that by ascribing to three different particles either one of two properties, we necessarily end up in a situation when at least two of the particles have the same property. In quantum physics, this principle is violated in experiments involving postselection of the particles in appropriately-chosen states. Here, we give two explicit constructions using standard gates and measurements that illustrate this fact. Intriguingly, the procedures described are manifestly non-local, which demonstrates that the correlations needed to observe the violation of this principle can be created without direct interactions between particles. Full article
(This article belongs to the Special Issue Quantum Nonlocality)
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Open AccessArticle Quantum Dynamics and Non-Local Effects Behind Ion Transition States during Permeation in Membrane Channel Proteins
Entropy 2018, 20(8), 558; https://doi.org/10.3390/e20080558
Received: 30 April 2018 / Revised: 19 July 2018 / Accepted: 23 July 2018 / Published: 27 July 2018
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Abstract
We present a comparison of a classical and a quantum mechanical calculation of the motion of K+ ions in the highly conserved KcsA selectivity filter motive of voltage gated ion channels. We first show that the de Broglie wavelength of thermal ions
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We present a comparison of a classical and a quantum mechanical calculation of the motion of K+ ions in the highly conserved KcsA selectivity filter motive of voltage gated ion channels. We first show that the de Broglie wavelength of thermal ions is not much smaller than the periodic structure of Coulomb potentials in the nano-pore model of the selectivity filter. This implies that an ion may no longer be viewed to be at one exact position at a given time but can better be described by a quantum mechanical wave function. Based on first principle methods, we demonstrate solutions of a non-linear Schrödinger model that provide insight into the role of short-lived (~1 ps) coherent ion transition states and attribute an important role to subsequent decoherence and the associated quantum to classical transition for permeating ions. It is found that short coherences are not just beneficial but also necessary to explain the fast-directed permeation of ions through the potential barriers of the filter. Certain aspects of quantum dynamics and non-local effects appear to be indispensable to resolve the discrepancy between potential barrier height, as reported from classical thermodynamics, and experimentally observed transition rates of ions through channel proteins. Full article
(This article belongs to the Special Issue Quantum Nonlocality)
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Open AccessArticle On the Significance of the Quantum Mechanical Covariance Matrix
Entropy 2018, 20(7), 500; https://doi.org/10.3390/e20070500
Received: 30 May 2018 / Revised: 24 June 2018 / Accepted: 26 June 2018 / Published: 28 June 2018
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Abstract
The characterization of quantum correlations, being stronger than classical, yet weaker than those appearing in non-signaling models, still poses many riddles. In this work, we show that the extent of binary correlations in a general class of nonlocal theories can be characterized by
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The characterization of quantum correlations, being stronger than classical, yet weaker than those appearing in non-signaling models, still poses many riddles. In this work, we show that the extent of binary correlations in a general class of nonlocal theories can be characterized by the existence of a certain covariance matrix. The set of quantum realizable two-point correlators in the bipartite case then arises from a subtle restriction on the structure of this general covariance matrix. We also identify a class of theories whose covariance has neither a quantum nor an “almost quantum” origin, but which nevertheless produce the accessible two-point quantum mechanical correlators. Our approach leads to richer Bell-type inequalities in which the extent of nonlocality is intimately related to a non-additive entropic measure. In particular, it suggests that the Tsallis entropy with parameter q=1/2 is a natural operational measure of non-classicality. Moreover, when generalizing this covariance matrix, we find novel characterizations of the quantum mechanical set of correlators in multipartite scenarios. All these predictions might be experimentally validated when adding weak measurements to the conventional Bell test (without adding postselection). Full article
(This article belongs to the Special Issue Quantum Nonlocality)
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Open AccessArticle GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality
Entropy 2018, 20(6), 478; https://doi.org/10.3390/e20060478
Received: 21 March 2018 / Revised: 6 June 2018 / Accepted: 6 June 2018 / Published: 20 June 2018
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Abstract
We review an argument that bipartite “PR-box” correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger–Horne–Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask
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We review an argument that bipartite “PR-box” correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger–Horne–Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask whether the argument extends to GHZ correlations. If it does—i.e., if it shows that GHZ correlations violate relativistic causality in the classical limit—then the argument must be incorrect (since GHZ correlations do respect relativistic causality in the classical limit.) However, we find that the argument does not extend to GHZ correlations. We also show that both PR-box correlations and GHZ correlations can be retrocausal, but the retrocausality of PR-box correlations leads to self-contradictory causal loops, while the retrocausality of GHZ correlations does not. Full article
(This article belongs to the Special Issue Quantum Nonlocality)
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Open AccessArticle Capacity and Entropy of a Retro-Causal Channel Observed in a Twin Mach-Zehnder Interferometer During Measurements of Pre- and Post-Selected Quantum Systems
Entropy 2018, 20(6), 411; https://doi.org/10.3390/e20060411
Received: 20 April 2018 / Revised: 18 May 2018 / Accepted: 23 May 2018 / Published: 27 May 2018
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Abstract
Simple intuitive models are presented for the capacity and entropy of retro-causal channels in measured ensembles of quantum systems which can be represented as statistical mixtures of pre-selected only and pre- and post-selected systems. Measurement data from a twin Mach-Zehnder interferometer experiment are
[...] Read more.
Simple intuitive models are presented for the capacity and entropy of retro-causal channels in measured ensembles of quantum systems which can be represented as statistical mixtures of pre-selected only and pre- and post-selected systems. Measurement data from a twin Mach-Zehnder interferometer experiment are used in these models to discuss the capacity and entropy of an apparent retro-causal channel observed in the experimental data. It is noted that low capacity/low entropy retro-causal channels can exist in strong measurement systems. Full article
(This article belongs to the Special Issue Quantum Nonlocality)
Open AccessArticle Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment
Entropy 2018, 20(4), 299; https://doi.org/10.3390/e20040299
Received: 27 February 2018 / Revised: 11 April 2018 / Accepted: 12 April 2018 / Published: 19 April 2018
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Abstract
The Stern–Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or
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The Stern–Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C ( z , θ ) by redefining the Banaszek–Wódkiewicz correlation in terms of the Wigner operator, that is C ( z , θ ) = Ψ | W ^ ( z , p z ) σ ^ ( θ ) | Ψ , where W ^ ( z , p z ) is the Wigner operator, σ ^ ( θ ) is the Pauli spin operator in an arbitrary direction θ and | Ψ is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser–Horne–Shimony–Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality. Full article
(This article belongs to the Special Issue Quantum Nonlocality)
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