As part of a challenge to critics of Bell's analysis of the EPR argument, framed in the form of a bet, R. D. Gill formulated criteria to assure that all non-locality is precluded from simulation-algorithms used to test Bell's theorem. This is achieved in part by parceling out the subroutines for the source and both detectors to three separate computers. He argues that, in light of Bell's theorem, following these criteria absolutely precludes mimicking EPR-B correlations as computed with Quantum Mechanics and observed in experiments. Herein, nevertheless, we describe just such an local algorithm, fully faithful to his criteria, that yields results mimicking exactly quantum correlations. We observe that our simulation-algorithm succeeds by altering an implicit assumption made by Bell to the equivalent effect that the source of EPR pairs is a single Poisson process followed by deterministic detection. Instead we assume the converse, namely that the source is deterministic but detection involves multiple, independent Poisson processes, one at each detector with an intensity given by Malus' Law. Finally, we speculate on some consequences this might have for quantum computing algorithms.
Beginning with the Bell theorem, cyclic systems of dichotomous random variables have been the object of many foundational findings in quantum mechanics. Here, we ask the question: if one chooses a cyclic system "at random" (uniformly within the hyperbox of all possible systems with given marginals), what are the odds that it will be contextual? We show that the odds of contextuality rapidly tend to zero as the size of the system increases. The result is based on the Contextuality-by-Default theory, in which we do not have to assume that the systems are subject to the no-disturbance/no-signalin…
The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of \emph{signal locality} plus \emph{predictability} are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each other -- it…
A recent claim (Deutsch and Hayden (2000)), that non-locality can be refuted by considering the evolution of the system in the Heisenberg picture, is denied. What they demonstrated was not the falsity of non-locality but the no-superluminal-signalling principle.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics…
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell's inequality are locality and counterfactual definiteness, but not scientific realism, determinism, or hidden …
Non-locality sharing for a three-qubit system via multilateral sequential measurements was deeply discussed. Different from 2-qubit case, it is shown that non-locality sharing between $\mathrm{Alice_{1}-Bob_{1}-Charlie_{1}}$ and $\mathrm{Alice_{2}-Bob_{2}-Charlie_{2}}$ in 3-qubit system can be observed, where two Mermin-Ardehali-Belinskii-Klyshko (MABK) inequalities can be violated simultaneously. What's more, a complete non-locality sharing with 8 MABK inequalities violations simultaneously can be also observed. Compared with 2-qubit case, the nonlocal sharing in a three qubit system shows mo…
We address the problem of detecting non-locality in coupled N level systems in the language of spin. Through a number of examples, we show that non-locality can be detected via a violation of the standard Bell inequality, irrespective of what N is, with correlations from observables of order k ~ 2s in the fundamental spin operators. We further show that, contrarily, if the order k is frozen, then non-locality eludes a detection when s >> k, leading to a weak classical limit. Armed with these results, we proceed to characterize observables that 'genuinely' reflect non-locality in higher dimensi…
By studying generalized non-signalling theories, the hope is to find out what makes quantum mechanics so special. In the present paper, we revisit the paradigmatic model of non-signalling boxes and introduce the concept of a genuine box. This will allow us to present the first generalized non-signalling model featuring quantum-like dynamics. In particular, we present the coupler, a device enabling non-locality swapping, the analogue of quantum entanglement swapping, as well as teleportation. Remarkably, part of the boundary between quantum and post-quantum correlations emerges in our study.
We consider entropy in Generalized Non-Signalling Theory (also known as box world) where the most common definition of entropy is the measurement entropy. In this setting, we completely characterize the set of allowed entropies for a bipartite state. We find that the only inequalities amongst these entropies are subadditivity and non-negativity. What is surprising is that non-locality does not play a role - in fact any bipartite entropy vector can be achieved by separable states of the theory. This is in stark contrast to the case of the von Neumann entropy in quantum theory, where only entang…
We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism whereby it is the entanglement of the modes that can be populated by the particles what really matters and not the particles themselves. Indeed, by means of a metr…
Loophole-free experiments have demonstrated that at least one of three features is false when the violation of Bell's inequalities is observed: Locality, Realism or (what is lesser known) Ergodicity. An experiment is proposed to find out, or at least to get an indication about, which one is false. It is based on recording the time evolution of the rate of series of outcomes that are found not-random in a pulsed Bell's setup. The results of such experiment would be important not only to the foundations of Quantum Mechanics. For, even if the foundational issue remained not fully decided, they wo…
We discuss quantum non-locality and contextuality using the notion of transition sets. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear graphical illustration of what violations of Bell inequalities quantify. In particular, we show graphically how these violations are related to measures of non-local transition sets. We also introduce a new form of contextuality, {\em measurement ordering contextuality}, i.e. there exists commuting operators $\hat{\mathcal{A}}$ and $\hat{\mathcal{B}}$ such t…
The quest for fundamental test of quantum mechanics is an ongoing effort. We here address the question of what are the lowest possible moments needed to prove quantum nonlocality and noncontextuality without any further assumption -- in particular without the often assumed dichotomy. We first show that second order correlations can always be explained by a classical noncontextual local-hidden-variable theory. Similar third-order correlations also cannot violate classical inequalities in general, except for a special state-dependent noncontextuality. However, we show that fourth-order correlati…
Non-locality, or quantum-non-locality, are buzzwords in the community of quantum foundation and information scientists, which purportedly describe the implications of Bell's theorem. When such phrases are treated seriously, that is it is claimed that Bell's theorem reveals non-locality as an inherent trait of the quantum description of the micro-world, this leads to logical contradictions, which will be discussed here. In fact, Bell's theorem, understood as violation of Bell inequalities by quantum predictions, is consistent with Bohr's notion of complementarity. Thus, if it points to anything…
Maudlin has claimed that no local theory can reproduce the predictions of standard quantum mechanics that violate Bell's inequality for Bohm's version (two spin-half particles in a singlet state) of the Einstein-Podolsky-Rosen problem. It is argued that, on the contrary, standard quantum mechanics itself is a counterexample to Maudlin's claim, because it is local in the appropriate sense (measurements at one place do not influence what occurs elsewhere there) when formulated using consistent principles in place of the inconsistent appeals to "measurement" found in current textbooks. This argum…
In all local realistic theories worked out till now, locality is considered as a basic assumption. Most people in the field consider the inconsistency between local realistic theories and quantum mechanics to be a result of non-local nature of quantum mechanics. In this paper, we derive Bell's inequality for particles with instantaneous interactions, and show that the aforementioned contradiction still exists between quantum mechanics and non-local hidden variable models. Then, we use this non-locality to obtain the GHZ theorem. In what follows, we show that Bacon and Toner's protocol, for the…
It is demonstrated that hidden variables of a certain type follow logically from a certain local causality requirement (``Bell Locality'') and the empirically well-supported predictions of quantum theory for the standard EPR-Bell setup. The demonstrated hidden variables are precisely those needed for the derivation of the Bell Inequalities. We thus refute the widespread view that empirical violations of Bell Inequalities leave open a choice of whether to reject (i) locality or (ii) hidden variables. Both principles are indeed assumed in the derivation of the inequalities, but since, as we demo…
Using Bell-inequalities as a tool to explore non-classical physical behaviours, in this paper we analyze what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin-lattice, we want to know whether or not it is possible to violate a Bell-inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via co…
Encoding information in quantum systems can offer surprising advantages but at the same time there are limitations that arise from the fact that measuring an observable may disturb the state of the quantum system. In our work, we provide an in-depth analysis of a simple question: What happens when we perform two measurements sequentially on the same quantum system? This question touches upon some fundamental properties of quantum mechanics, namely the uncertainty principle and the complementarity of quantum measurements. Our results have interesting consequences, for example they can provide a…
Non-local correlations are not only a fascinating feature of quantum theory, but an interesting resource for information processing, for instance in communication-complexity theory or cryptography. An important question in this context is whether the resource can be distilled: Given a large amount of weak non-local correlations, is there a method to obtain strong non-locality using local operations and shared randomness? We partly answer this question by no: CHSH-type non-locality, the only possible non-locality of binary systems, which is not super-strong, but achievable by measurements on ce…
I present a simple two-party quantum communication complexity protocol with higher success rate than the best possible classical protocol for the same task. The quantum protocol is shown to be equivalent to a quantum non-locality test, except that it is not necessary to close the locality loophole. I derive bounds for the detector efficiency and background count rates necessary for an experimental implementation and show that they are close to what can be currently achieved using ion trap technology. I also analyze the requirements for a three-party protocol and show that they are less demandi…
Recently,the principle of nonviolation of information causality [Nature 461,1101 (2009)], has been proposed as one of the foundational properties of nature. We explore the Hardy's nonlocality theorem for two qubit systems, in the context of generalised probability theory, restricted by the principle of nonviolation of information causality. Applying, a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy's nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics,but stil…
The paper has two aims: (1) it sets out to show that it is well motivated to seek for an account of quantum non-locality in the framework of ontic structural realism (OSR), which integrates the notions of holism and non-separability that have been employed since the 1980s to achieve such an account. However, recent research shows that OSR on its own cannot provide such an account. Against this background, the paper argues that by applying OSR to the primitive ontology theories of quantum physics, one can accomplish that task. In particular, Bohmian mechanics offers the best prospect for doing …
Bell non-locality and Kochen-Specker (KS) contextuality are logically independent concepts, fuel different protocols with quantum vs classical advantage, and have distinct classical simulation costs. A natural question is what are the relations between these concepts, advantages, and costs. To address this question, it is useful to have a map that captures all the connections between Bell non-locality and KS contextuality in quantum theory. The aim of this work is to introduce such a map. After defining the theory-independent notions of Bell non-locality and KS contextuality for ideal measurem…
As a basis for epistemological study of ``time,'' we analyze three suspect phenomena introduced by modern physics: non-locality, asymmetric aging and advanced interaction. It is shown that all three arise in connection with what has to be taken as arbitrary ideosyncrasies in formulation. It is shown that minor changes result in internally consistent variations of both Quantum Mechanics and Special Relativity devoid of these phenomena. The reinterpretation of some experiments though to confirm the existence of non-locality and asymmetric aging is briefly considered and a possible test is propos…
Bohmian mechanics is an alternative interpretation of quantum mechanics. We outline the main characteristics of its non-relativistic formulation. Most notably it does provide a simple solution to the infamous measurement problem of quantum mechanics. Presumably the most common objection against Bohmian mechanics is based on its non-locality and its apparent conflict with relativity and quantum field theory. However, several models for a quantum field theoretical generalization do exist. We give a non-technical account of some of these models.
While initial versions of Bell's theorem captured the notion of locality with the assumption of factorizability, in later presentations, Bell argued that factorizability could be derived from the more fundamental principle of local causality. Here we show that, contrary to what is commonly assumed, in order to derive factorizability from the principle of local causality, a non-trivial assumption, similar but strictly independent of settings independence, is required. Loosely speaking, such an extra assumption demands independence between the states of the measurement apparatuses. We conclude t…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed computation is extended so as to apply quantum processing. This has been achieved in one of two distinct ways: (1) by initializing the system in a quantum entangled state, and/or (2) by applying quantum communication channels. In this paper, we explain why some of these prior claims are misleading, in the sense that they rely on changes to the model unrelated to quan…
The violation of Bell inequalities by quantum physical experiments disproves all relativistic micro causal, classically real models, short Local Realistic Models (LRM). Non-locality, the infamous "spooky interaction at a distance" (A. Einstein), is already sufficiently 'unreal' to motivate modifying the "realistic" in "local realistic". This has led to many worlds and finally many minds interpretations. We introduce a simple many world model that resolves the Einstein Podolsky Rosen paradox. The model starts out as a classical LRM, thus clarifying that the many worlds concept alone does not im…
It is well known that entangled quantum states can be nonlocal: the correlations between local measurements carried out on these states cannot always be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are even more nonlocal than bipartite ones in the sense that nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely we enquire what kinds of classical communicatio…
A local and deterministic model of quantum correlations is always possible, as shown explicitly by Brans in 1988: one simply needs the physical systems being measured to have a suitable statistical correlation with the physical systems performing the measurement, via some common cause. Hence, to derive no-go results such as Bell inequalities, an assumption of measurement independence is crucial. It is a surprisingly strong assumption -- less than 1/15 bits of prior correlation suffice for a local model of the singlet state of two qubits -- with ramifications for the security of quantum communi…
Experiments motivated by Bell's theorem have led some physicists to conclude that quantum theory is nonlocal. However, the theoretical basis for such claims is usually taken to be Bell's Theorem, which shows only that if certain predictions of quantum theory are correct, and a strong hidden-variable assumption is valid, then a certain locality condition must fail. This locality condition expresses the idea that what an experimenter freely chooses to measure in one spacetime region can have no effect of any kind in a second region situated spacelike relative to the first. The experimental resul…
The realization of the Einstein-Podolsky-Rosen effect by the correlation of spin projections of two particles created in the decay of a single scalar particle is considered for particles propagating in gravitational field. The absence of a global definition of spatial directions makes it unclear whether the correlation may exist in this case and, if yes, what directions in distant regions must be correlated. It is shown that in a gravitational field an approximate correlation may exist and the correlated directions are connected with each other by the parallel transport along the world lines o…
In the hidden measurement formalism that we develop in Brussels we explain the quantum structure as due to the presence of two effects, (a) a real change of state of the system under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement process. We show that the presence of these two effects leads to the major part of the quantum mechanical structure of a theory where the measurements contain the two mentioned effects. We present a quantum machine, where we can illustrate in a simple way how the quantum structure arises as a consequen…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we char…
Motivated by some recent news, a journalist asks a group of physicists: "What's the meaning of the violation of Bell's inequality?" One physicist answers: "It means that non-locality is an established fact". Another says: "There is no non-locality; the message is that measurement outcomes are irreducibly random". A third one says: "It cannot be answered simply on purely physical grounds, the answer requires an act of metaphysical judgement". Puzzled by the answers, the journalist keeps asking questions about quantum theory: "What is teleported in quantum teleportation?" "How does a quantum com…
We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measu…
We elaborate the new interpretation of quantum theory that we recently proposed, according to which quantum particles are considered conceptual entities mediating between pieces of ordinary matter which are considered to act as memory structures for them. Our aim is to identify what is the equivalent for the human cognitive realm of what physical space-time is for the realm of quantum particles and ordinary matter. For this purpose, we identify the notion of 'story' as the equivalent within the human cognitive realm of what ordinary matter is in the physical quantum realm, and analyze the role…
We explore a connection between monogamy of non-locality and a weak macroscopic locality condition: the locality of the average behaviour. These are revealed by our analysis as being two sides of the same coin. Moreover, we exhibit a structural reason for both in the case of Bell-type multipartite scenarios, shedding light on but also generalising the results in the literature [Ramanathan et al., Phys. Rev. Lett. 107, 060405 (2001); Pawlowski & Brukner, Phys. Rev. Lett. 102, 030403 (2009)]. More specifically, we show that, provided the number of particles in each site is large enough compared …
We discuss the implications of the principle of locality for interference in quantum field theory. As an example, we consider the interaction of two charges via a mediating quantum field and the resulting interference pattern, in the Lorenz gauge. Using the Heisenberg picture, we propose that detecting relative phases or entanglement between two charges in an interference experiment is equivalent to accessing empirically the gauge degrees of freedom associated with the so-called ghost (scalar) modes of the field in the Lorenz gauge. These results imply that ghost modes are measurable and hence…
We look at what type of arguments can rule out the joint reality (or value definiteness) of two observables of a physical system, such as a qubit, and give several strong yet simple no-go results based on assumptions typically weaker than those considered previously. The first result uses simple geometry combined with a locality assumption to derive device-independent steering inequalities. These may also be regarded as "conditional" Bell inequalities, are simpler in principle to test than standard Bell inequalities, and for two-qubit systems are related to properties of the quantum steering e…
Bell's inequality fundamentally changed our understanding of quantum mechanics. Bell's insight that non-local correlations between quantum systems cannot be explained classically can be verified experimentally, and has numerous applications in modern quantum information. Today, the CHSH inequality is probably the most well-known Bell inequality and it has given us a wealth of understanding in what differentiates the classical from the quantum world. Yet, there are certainly other means of quantifying "Bell non-locality without inequalities" such as the famous Hardy's paradox. As such, one may …
In a previous paper, we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe $M$, existing on timeless configuration space $\mathcal{M}$. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. To deal with the challenges gauge symmetries may pose to a good definition of locality, I start by demanding symmetries to have an action on $\mathcal{M}$ so that the quotient wrt the symmetries respects certain factorizations of $\mathcal{M}$. These factor…
The generation of series of random numbers is an important and difficult problem. Appropriate measurements on entangled states have been proposed as the definitive solution, based on the impossibility of exploiting quantum non locality to get faster than light signaling. There is a controversy regarding what is preferable to produce series with utilizable randomness in practice, high or low entanglement. We prepare biphotons with three different levels of entanglement, easy entangled, marginally entangled and no entangled. Randomness is evaluated, independently of the quantum non locality argu…
The discipline of parallelization in the manifold of all possible measurement results is shown to be responsible for the existence of all quantum correlations, with the upper bound on their strength stemming from the maximum of possible torsion within all norm-composing parallelizable manifolds. A profound interplay is thus uncovered between the existence and strength of quantum correlations and the parallelizability of the spheres S^0, S^1, S^3, and S^7 necessitated by the four real division algebras. In particular, parallelization within a unit 3-sphere is shown to be responsible for the exi…
Robert Griffiths has recently addressed, within the framework of a 'consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties of a system by establishing, instead, properties of a system modif…
The Bell's inequalities are derived from the hypotheses of Locality, Realism and (what is lesser known) the equality between the factual and the counterfactual time averages of the expectation values of observables. The necessity of a hypothesis additional to Local Realism opens a promising way out to the old controversy between Quantum Mechanics and Local Realism. For, it is possible to speculate that it is this additional hypothesis, and not Local Realism, what is disproved in the experiments reporting the violation of the Bell's inequalities. Yet, there are doubts on how the additional hypo…
It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not interact. Claims to the contrary based on quantum violations of Bell inequalities are shown to be incorrect. A specific example traces a violation of the CHSH Bell inequality in the case of a spin-3/2 particle to the noncommutation of certain quantum operators in a situation where (non)locality is not an issue. A consistent histories analysis of what quantum …
In the first part of this presentation (sections 2 to 6), I show that Bell's Inequalities provide a quantitative criterion to test "reasonable" Supplementary Parameters Theories versus Quantum Mechanics. Following Bell, I first explain the motivations for considering supplementary parameters theories: the argument is based on an analysis of the famous Einstein-Podolsky-Rosen (EPR) Gedankenexperiment . Introducing a reasonable Locality Condition, we will then derive Bell's theorem, which states: (i) that Local Supplementary Parameters Theories are constrained by Bell's Inequalities; (ii) that c…
The concept of the physical state of a system is ubiquitous in physics but is usually presented in terms of specific cases. For example, the state of a point particle of mass m is completely characterized by its position and momentum. There is a tendency to consider such states as "real", i.e., as physical properties of a system. This rarely causes problems in classical physics but the notion of real quantum states has contributed mightily to the philosophical conundrums associated with quantum mechanics. The Einstein-Rosen-Podolsky paradox is a prime example. In fact, quantum states are not p…
Colliders are not Testing Locality via Bell's Inequality nor Providing an Unconditional Proof of Entanglement
Institute for Particle Physics Phenomenology, and Department of Mathematical Sciences, Durham University（达勒姆大学数学科学系粒子物理现象学研究所）；Bethe Center for Theoretical Physics & Physikalisches Institut der Universität Bonn（波恩大学理论物理贝特中心与物理研究所）；Jožef Stefan Institute（约瑟夫斯蒂芬研究所）
This paper addresses arguments that "separability" is an assumption of Bell's theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as "holism") will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately. In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (b) the definition of Bell's locality condition…
We give an introduction to the theory of multi-partite entanglement. We begin by describing the "coordinate system" of the field: Are we dealing with pure or mixed states, with single or multiple copies, what notion of "locality" is being used, do we aim to classify states according to their "type of entanglement" or to quantify it? Building on the general theory of multi-partite entanglement - to the extent that it has been achieved - we turn to explaining important classes of multi-partite entangled states, including matrix product states, stabilizer and graph states, bosonic and fermionic G…
