A classical perspective on nonlocality in quantum field theory
Peter Morgan
备注：
14 pages, LaTeX; v3:reference to quant-ph/0111029 added to resolve lacuna. v4 purely clerical: ref to 0111029 changed to 0111027 (LANL changed # following day)
A classical statistical field theory hidden variable model for the quantized Klein-Gordon model is constructed that preserves relativistic signal locality and is relativistically covariant, but is at the same time relativistically nonlocal, paralleling the Hegerfeldt nonlocality of quantum theory. It is argued that the relativistic nonlocality of this model is acceptable to classical physics, but in any case the approach taken here characterizes the nonlocality of the quantized Klein-Gordon model in terms of concepts from classical statistical field theory.
Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems…
Nonlocality is a property of paramount importance both conceptually and computationally exhibited by quantum systems, which has no classical counterpart. Conceptually, it is important because it implies that the evolving system has information on what happens at any space point and time. Computationally, because such a knowledge makes any calculation intractable as the number of degrees of freedom involved increases beyond a few of them. Bohmian mechanics, with its trajectory-based formalism in real configuration space, can help to better understand nonlocality. A detailed analysis of how nonl…
The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a ''particle'', which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or ''cybernetic'', relationships between ''particles'' and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.
For two bipartite pure states, we consider the problem of unambiguous identification without classical knowledge on the states. The optimal success probability by means of local operations and classical communication is shown to be less than the maximum attainable by the global measuring scheme.
It is shown that classical electrodynamics in its alternative Kemmer-Duffin-Petiau-Harish-Chandra formulation surprisingly reveals a Hilbert space structure leading to the possibility of entangled states of classical radiation, and this in turn implies the violation of Einstein-Bell locality in spite of Lorentz invariance.
With the advent of device independent quantum information processing, nonlocality is nowadays regarded as a resource to implement various tasks. On the analogy of entanglement theory we approach nonlocality from this perspective. In order to do so, we analyze in full detail the operations that can be implemented in this scenario and under which nonlocality cannot increase. This provides a theoretical ground to study how to order and quantify nonlocal behaviours. Finally, we review several nonlocality measures and discuss their validity from this point of view.
In this thesis, we study about three subjects 1- Classical simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements, 2- Quantum correlations in successive single spin measurements, 3- Non locality without inequality for almost all two-qubit entangled states based on Cabello's non locality argument.
We analyze interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that "quantum nonlocality" is the basic factor differing quantum and classical realizations of entanglement. Instead, we point to the breakthrough Grangier et al. experiment on coincidence detection which was done in 1986 and played the crucial role in rejection of (semi-)classical field models in favor of quantum mechanics. Classical entanglement sources produce light beams with the coeffic…
We present a two-player communication task that can be solved by a protocol of polylogarithmic cost in the simultaneous message passing model with classical communication and shared entanglement, but requires exponentially more communication in the classical interactive model. Our second result is a two-player nonlocality game with input length $n$ and output of polylogarithmic length, that can be won with probability 1-o(1) by players sharing polylogarithmic amount of entanglement. On the other hand, the game is lost with probability $Ω(1)$ by players without entanglement, even if they are al…
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an {\em a priori} different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure comm…
The certification of Bell nonlocality or quantum steering implies the use of incompatible measurements. Here we make this connection quantitative. We show how to strengthen robustness-based steering and nonlocality quantifiers in order that they give strong lower bounds to previously proposed incompatibility quantifiers. Our results can be seen from two perspectives. On the one hand, they can be used to estimate how much steering or nonlocality can be demonstrated with a given set of measurements. On the other hand, they gives one-sided device-independent and device-independent ways of estimat…
The upper bound of the fine-grained uncertainty relation is different for classical physics, quantum physics and no-signaling theories with maximal nonlocality (supper quantum correlation), as was shown in the case of bipartite systems [J. Oppenheim and S. Wehner, Science 330, 1072 (2010)]. Here, we extend the fine-grained uncertainty relation to the case of tripartite systems. We show that the fine-grained uncertainty relation determines the nonlocality of tripartite systems as manifested by the Svetlichny inequality, discriminating between classical physics, quantum physics and super quantum…
In a recent work, it was shown by one of us (EGC) that Bell-Kochen-Specker inequality violations in phenomena satisfying the no-disturbance condition (a generalisation of the no-signalling condition) cannot in general be explained with a faithful classical causal model -- that is, a classical causal model that satisfies the assumption of no fine-tuning. The proof of that claim however was restricted to Bell scenarios involving 2 parties or Kochen-Specker-contextuality scenarios involving 2 measurements per context. Here we show that the result holds in the general case of arbitrary numbers of …
Quantum nonlocality is an inherently non-classical feature of quantum mechanics and manifests itself through violation of Bell inequalities for nonlocal games. We show that in a fairly general setting, a simple extension of a nonlocal game can certify instead the absence of quantum nonlocality. Through contraposition, our result implies that a super-classical performance for such a game ensures that a player's output is unpredictable to the other player. Previously such output unpredictability was known with respect to a third party.
The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question: how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce a n…
Due to the importance of entanglement for quantum information purposes, a framework has been developed for its characterization and quantification as a resource based on the following operational principle: entanglement among $N$ parties cannot be created by local operations and classical communication, even when $N-1$ parties collaborate. More recently, nonlocality has been identified as another resource, alternative to entanglement and necessary for device-independent quantum information protocols. We introduce an operational framework for nonlocality based on a similar principle: nonlocalit…
What violations of Bell inequalities teach us is that the world is quantum mechanical, i.e., nonclassical. Assertions that they imply the world is nonlocal arise from ignoring differences between quantum and classical physics.
Complementarity and nonlocality are two characteristic traits of quantum physics that distinguishes it from classical physics. In this paper, we prove that the complementarity between global and local observables in Bell's experiment sets the decisive foundation for the nonlocality of composite systems.
Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.
In several recent communications (Khrennikov 2019a, b, c, 2020a, b), A. Khrennikov argued for "eliminating the issue of quantum nonlocality" from the analysis of quantum entanglement and quantum phenomena in general. He proposed to differentiate quantum and classical phenomena and entanglement not by their respective nonlocality and locality, as is common, but by the discreteness of quantum phenomena vs. the continuity of classical phenomena, supplemented by Bohr's complementarity in the case of quantum phenomena. As I argue here, however, the question may not be that of "eliminating the issue…
It is shown that the ensemble $\{p (α),|α>|α^*>\}$ where $p (α)$ is a Gaussian distribution of finite variance and $| α>$ is a coherent state can be better discriminated with an entangled measurement than with any local strategy supplemented by classical communication. Although this ensemble consists of products of quasi-classical states, it exhibits some quantum nonlocality. This remarkable effect is demonstrated experimentally by implementing the optimal local strategy together with a joint nonlocal strategy that yields a higher fidelity.
We discuss a connection between Bell nonlocality and Bayesian games. This link offers interesting perspectives for Bayesian games, namely to allow the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signaling boxes. The possibility of having such 'nonlocal advice' will lead to novel joint strategies, impossible to achieve in the classical setting. This implies that quantum resources, or more general no-signaling resources, offer a genuine advantage over classical ones. Moreover, some of these strategies can repre…
Quantum separable operations are defined as those that cannot produce entanglement from separable states, and it is known that they strictly surpass local operations and classical communication (LOCC) in a number of tasks, which is sometimes referred to as "quantum nonlocality without entanglement." Here we consider a task with such a gap regarding the trade-off between state discrimination and preservation of entanglement. We show that this task along with the gap has an analogue in a purely classical setup, indicating that the quantum properties are not essential in the existence of a nonzer…
Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem has been a central theme of research from a variety of perspectives, mainly motivated by quantum information science, where the nonlocality of quantum theory underpins many of the advantages afforded by a quantum processing of information. The focus of this review is to a large extent oriented by these later developments. We review the main concepts and tools …
For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detector…
Nonlocality enables two parties to win specific games with probabilities strictly higher than allowed by any classical theory. Nevertheless, all known such examples consider games where the two parties have a common interest, since they jointly win or lose the game. The main question we ask here is whether the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We answer this in the affirmative by presenting a simple conflicting interest game, where quantum strategies outperform classical ones. Moreover, we show that our …
Bell nonlocality from compatibility of entanglement-breaking channels
Hon Hai (Foxconn) Quantum Computing Research Center（鸿海（富士康）量子计算研究中心）；Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University（国立成功大学物理系与量子前沿研究技术中心）；H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学H.H.威尔斯物理实验室）；ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）
An interesting protocol for classical teleportation of an unknown classical state was recently suggested by Cohen, and by Gour and Meyer. In that protocol, Bob can sample from a probability distribution P that is given to Alice, even if Alice has absolutely no knowledge about P. Pursuing a similar line of thought, we suggest here a limited form of nonlocality - "classical nonlocality". Our nonlocality is the (somewhat limited) classical analogue of the Hughston-Jozsa-Wootters (HJW) quantum nonlocality. The HJW nonlocality tells us how, for a given density matrix rho, Alice can generate any rho…
We explore correlation polytopes to derive a set of all Boole-Bell type conditions of possible classical experience which are both maximal and complete. These are compared with the respective quantum expressions for the Greenberger-Horne-Zeilinger (GHZ) case and for two particles with spin state measurements along three directions.
The view exists that the Bell inequality is a mere inconsistent application of classical concepts to a well-established quantum world. In the article, ``Nonlocality claims are inconsistent with Hilbert-space quantum mechanics'' [Phys. Rev. A, 101, 022117, (2020)], Robert B. Griffiths advocates for quantum theory's locality. Although R. B. Griffiths presents valuable insights in favor of quantum mechanics' local character, he argues the Bell inequality is an inconsistent application of classical physics to quantum mechanics. We explain why a correct assessment of the Bell inequality does not in…
In this paper, combined with infinite time-evolving block decimation (iTEBD) algorithm and Bell-type inequalities, we investigate multi-partite quantum nonlocality in an infinite one-dimensional quantum spin-1/2 XXZ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, meanwhile only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped anti-ferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order QPT (or …
We outline the general construction of three-players games with incomplete information which fulfil the following conditions: (i) symmetry with respect to the exchange of the players; (ii) the existence of the upper bound for total payoff resulting from Bell inequalities; (iii) the existence of both fair and unfair Nash equilibria saturating this bound. Conditions (i)$÷$(iii) imply that we are dealing with conflicting interest games. An explicit example of such a game is given. A quantum counterpart of this game is considered which is obtained by keeping the same utilities but replacing classi…
This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to determine the quantum limit of Bell-type linear inequalities. In contrast to semidefinite programming approaches, our method allows for the consideration of inequalities with abstract weights, by means of leveraging the Hermiticity of quantum states. Recognizing that classical correlations correspond to measurements made on separable states, we also introduce a pr…
The simulation of quantum correlations with alternative nonlocal resources, such as classical communication, gives a natural way to quantify their nonlocality. While multipartite nonlocal correlations appear to be useful resources, very little is known on how to simulate multipartite quantum correlations. We present the first known protocol that reproduces 3-partite GHZ correlations with bounded communication: 3 bits in total turn out to be sufficient to simulate all equatorial Von Neumann measurements on the 3-partite GHZ state.
We use techniques for lower bounds on communication to derive necessary conditions (in terms of detector efficiency or amount of super-luminal communication) for being able to reproduce the quantum correlations occurring in EPR-type experiments with classical local hidden-variable theories. As an application, we consider n parties sharing a GHZ-type state and show that the amount of super-luminal classical communication required to reproduce the correlations is at least n(log n - 3) bits and the maximum detector efficiency eta* for which the resulting correlations can still be reproduced by a …
We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed "quantum nonlocality without entanglement." We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72(2), compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.
Bell proved that quantum entanglement enables two space-like separated parties to exhibit classically impossible correlations. Even though these correlations are stronger than anything classically achievable, they cannot be harnessed to make instantaneous (faster than light) communication possible. Yet, Popescu and Rohrlich have shown that even stronger correlations can be defined, under which instantaneous communication remains impossible. This raises the question: Why are the correlations achievable by quantum mechanics not maximal among those that preserve causality? We give a partial answe…
We consider unambiguous discrimination of two separable bipartite states, one being pure and the other being a rank-2 mixed state. There is a gap between the optimal success probability under global measurements and the one achieved by generalized measurements with separable measurement operators. We show that even the latter success probability cannot be achieved via local operations and classical communication, leaving a nonzero gap in between.
Quantum nonlocality is revisited from a novel point of view by studying the problem of an originally classical particle immersed in the stochastic zero-point radiation field (zpf). The entire system is left to evolve until it reaches a state in which the radiative terms cancel each other in the mean in a first approximation. The ensuing approximate statistical description reduced to the particle's configuration space contains a nonclassical term due to the dispersion of the momentum, which depends on the density of particles ρ(x) and thus is nonlocal. This description is shown to be equivalent…
Quantum nonlocality and quantum steering are fundamental correlations of quantum systems which can not be created using classical resources only. Nonlocality describes the ability to influence the possible results of measurements carried out in distant systems, in quantum steering Alice remotely steers Bob's state. Research in nonlocality and steering possess a fundamental interest for the development of quantum information and in many applications requiring nonlocal resources like quantum key distribution. On the other hand, the Stern-Gerlach experiment holds an important place in the history…
Quantum nonlocality may be an artifact of the assumption that observers obey the laws of classical mechanics, while observed systems obey quantum mechanics. I show that, at least in the case of Bell's Theorem, locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the Many-Worlds Interpretation. Using the MWI, I shall show that the apparently "non-local" expectation value for the product of the spins of two widely separated particles --- the "quantum" part of Bell's Theorem --- is really due to a series of three purely local measurements. Thus, experime…
