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Special Issue "Quantum Nonlocality"

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

Deadline for manuscript submissions: closed (31 January 2019)

Printed Edition Available!
A printed edition of this Special Issue is available here.

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
Phone: +972545908806
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

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Keywords

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

Published Papers (16 papers)

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Editorial

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Open AccessEditorial
Quantum Nonlocality
Entropy 2019, 21(5), 447; https://doi.org/10.3390/e21050447
Received: 23 April 2019 / Accepted: 24 April 2019 / Published: 29 April 2019
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Abstract
The role of physics is to explain observed phenomena [...] Full article
(This article belongs to the Special Issue Quantum Nonlocality) Printed Edition available

Research

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Open AccessArticle
The Einstein–Podolsky–Rosen Steering and Its Certification
Entropy 2019, 21(4), 422; https://doi.org/10.3390/e21040422
Received: 17 January 2019 / Revised: 3 April 2019 / Accepted: 16 April 2019 / Published: 20 April 2019
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Abstract
The Einstein–Podolsky–Rosen (EPR) steering is a subtle intermediate correlation between entanglement and Bell nonlocality. It not only theoretically completes the whole picture of non-local effects but also practically inspires novel quantum protocols in specific scenarios. However, a verification of EPR steering is still [...] Read more.
The Einstein–Podolsky–Rosen (EPR) steering is a subtle intermediate correlation between entanglement and Bell nonlocality. It not only theoretically completes the whole picture of non-local effects but also practically inspires novel quantum protocols in specific scenarios. However, a verification of EPR steering is still challenging due to difficulties in bounding unsteerable correlations. In this survey, the basic framework to study the bipartite EPR steering is discussed, and general techniques to certify EPR steering correlations are reviewed. Full article
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Open AccessArticle
Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing
Entropy 2019, 21(2), 185; https://doi.org/10.3390/e21020185
Received: 15 December 2018 / Revised: 12 February 2019 / Accepted: 12 February 2019 / Published: 15 February 2019
Cited by 2 | PDF Full-text (367 KB) | HTML Full-text | XML Full-text
Abstract
The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell’s seminal work to distinguish, [...] Read more.
The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell’s seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method—initially developed for performing a hypothesis test of local-hidden-variable theories—can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test. Full article
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Open AccessArticle
Bell Inequalities with One Bit of Communication
Entropy 2019, 21(2), 171; https://doi.org/10.3390/e21020171
Received: 13 December 2018 / Revised: 28 January 2019 / Accepted: 6 February 2019 / Published: 13 February 2019
Cited by 1 | PDF Full-text (384 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We developed a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult. Using this method, we partially solved [...] Read more.
We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We developed a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult. Using this method, we partially solved the scenario where Alice and Bob choose between three inputs, finding a total of 668 inequivalent facet inequalities (with respect to relabelings of inputs and outputs). We also show that some of these inequalities are constructed from facet inequalities found in scenarios without communication, that is, the well-known Bell inequalities. Full article
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Open AccessArticle
Efficient Quantum Teleportation of Unknown Qubit Based on DV-CV Interaction Mechanism
Entropy 2019, 21(2), 150; https://doi.org/10.3390/e21020150
Received: 13 December 2018 / Revised: 30 January 2019 / Accepted: 1 February 2019 / Published: 5 February 2019
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Abstract
We propose and develop the theory of quantum teleportation of an unknown qubit based on the interaction mechanism between discrete-variable (DV) and continuous-variable (CV) states on highly transmissive beam splitter (HTBS). This DV-CV interaction mechanism is based on the simultaneous displacement of the [...] Read more.
We propose and develop the theory of quantum teleportation of an unknown qubit based on the interaction mechanism between discrete-variable (DV) and continuous-variable (CV) states on highly transmissive beam splitter (HTBS). This DV-CV interaction mechanism is based on the simultaneous displacement of the DV state on equal in absolute value, but opposite in sign displacement amplitudes by coherent components of the hybrid in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary modes. The relative phase of the displaced unknown qubit in the measurement number state basis can vary on opposite, depending on the parity of the basis states in the case of the negative amplitude of displacement that is akin to action of nonlinear effect on the teleported qubit. All measurement outcomes of the quantum teleportation are distinguishable, but the teleported state at Bob’s disposal may acquire a predetermined amplitude-distorting factor. Two methods of getting rid of the factors are considered. The quantum teleportation is considered in various interpretations. A method for increasing the efficiency of quantum teleportation of an unknown qubit is proposed. Full article
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Open AccessArticle
Non-Classical Correlations in n-Cycle Setting
Entropy 2019, 21(2), 134; https://doi.org/10.3390/e21020134
Received: 14 December 2018 / Revised: 28 January 2019 / Accepted: 30 January 2019 / Published: 1 February 2019
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Abstract
Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial [...] Read more.
Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the n-cycle setting. In particular, we focus on correlations manifested by Kochen–Specker–Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu–Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle setting, and the condition for the quantum violation for odd as well as even n-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and n-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction. Full article
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Open AccessArticle
Discrimination of Non-Local Correlations
Entropy 2019, 21(2), 104; https://doi.org/10.3390/e21020104
Received: 15 December 2018 / Revised: 11 January 2019 / Accepted: 17 January 2019 / Published: 23 January 2019
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Abstract
In view of the importance of quantum non-locality in cryptography, quantum computation, and communication complexity, it is crucial to decide whether a given correlation exhibits non-locality or not. As proved by Pitowski, this problem is NP-complete, and is thus computationally intractable unless NP [...] Read more.
In view of the importance of quantum non-locality in cryptography, quantum computation, and communication complexity, it is crucial to decide whether a given correlation exhibits non-locality or not. As proved by Pitowski, this problem is NP-complete, and is thus computationally intractable unless NP is equal to P. In this paper, we first prove that the Euclidean distance of given correlations from the local polytope can be computed in polynomial time with arbitrary fixed error, granted the access to a certain oracle; namely, given a fixed error, we derive two upper bounds on the running time. The first bound is linear in the number of measurements. The second bound scales with the number of measurements to the sixth power. The former holds only for a very high number of measurements, and is never observed in the performed numerical tests. We, then, introduce a simple algorithm for simulating the oracle. In all of the considered numerical tests, the simulation of the oracle contributes with a multiplicative factor to the overall running time and, thus, does not affect the sixth-power law of the oracle-assisted algorithm. Full article
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Open AccessArticle
Parallel Lives: A Local-Realistic Interpretation of “Nonlocal” Boxes
Entropy 2019, 21(1), 87; https://doi.org/10.3390/e21010087
Received: 1 July 2018 / Revised: 10 January 2019 / Accepted: 11 January 2019 / Published: 18 January 2019
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Abstract
We carry out a thought experiment in an imaginary world. Our world is both local and realistic, yet it violates a Bell inequality more than does quantum theory. This serves to debunk the myth that equates local realism with local hidden variables in [...] Read more.
We carry out a thought experiment in an imaginary world. Our world is both local and realistic, yet it violates a Bell inequality more than does quantum theory. This serves to debunk the myth that equates local realism with local hidden variables in the simplest possible manner. Along the way, we reinterpret the celebrated 1935 argument of Einstein, Podolsky and Rosen, and come to the conclusion that they were right in their questioning the completeness of the Copenhagen version of quantum theory, provided one believes in a local-realistic universe. Throughout our journey, we strive to explain our views from first principles, without expecting mathematical sophistication nor specialized prior knowledge from the reader. Full article
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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
Cited by 3 | PDF Full-text (568 KB) | HTML Full-text | XML Full-text
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 [...] Read more.
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
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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
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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 [...] Read more.
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
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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 [...] Read more.
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
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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
Cited by 2 | PDF Full-text (276 KB) | HTML Full-text | XML Full-text
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 [...] Read more.
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
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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
Cited by 1 | PDF Full-text (369 KB) | HTML Full-text | XML Full-text
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 [...] Read more.
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
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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
Cited by 1 | PDF Full-text (233 KB) | HTML Full-text | XML Full-text
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
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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
Cited by 2 | PDF Full-text (953 KB) | HTML Full-text | XML Full-text
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 [...] Read more.
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
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