Marek Zukowski, Ryszard Horodecki, Michal Horodecki, Pawel Horodecki
The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are explicitly derived. The violation of local realism in the case of ``hidden nonlocality'' is illustrated by an operational example.
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Generalised quantum measurements with two outcomes are fully characterised by two real parameters, dubbed as sharpness parameter and biasedness parameter and they can be linked with different aspects of the experimental setup. It is known that precision of measurements, characterised by the sharpness parameter of the measurements, reduces the possibility of probing quantum features like violation of local-realism (LR) or macro-realism (MR). Here we investigate the effect of biasedness together with sharpness of measurement and find a trade-off between those two parameters in the context of pro…
We show that quantum mechanics predicts a contradiction with local hidden variable theories for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new premise, macroscopic local realism.
We suggest to test the premise of ``macroscopic local realism'' which is sufficient to derive Bell inequalities when measurements of photon number are only accurate to an uncertainty of order $n$ photons, where $n$ is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' which have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of ``macroscopic local realism''. Quantum states violating th…
The conjecture is made that quantum mechanics is compatible with local hidden variables (or local realism). The conjecture seems to be ruled out by the theoretical argument of Bell, but it is supported by the empirical fact that nobody has been able to perform a loophole-free test of local realism in spite of renewed effort during almost 40 years.
A necessary and natural change in our application of quantum mechanics to separated systems is shown to reconcile quantum mechanics and local realism. An analysis of separation and localization justifies the proposed change in application of quantum mechanics. An important EPRB experiment is reconsidered and it is seen that when it is correctly interpreted it supports local realism. This reconciliation of quantum mechanics with local realism allows the axiom sets of quantum mechanics, probability, and special relativity to be joined in a consistent global axiom set for physics.
Quantum mechanics is strictly incompatible with local realism. It has been shown by Bell and others that it is possible, in principle, to experimentally differentiate between local realism and quantum mechanics. Numerous experiments have attempted to falsify local realism; however, they have consistently failed to close the detection loophole under strict locality conditions, thereby allowing local realistic explanations for their observations. In 2015, three experiments took place that tested local realism without the impediments of these significant loopholes. Between these three experiments…
Hardy's is one of the simplest arguments concerning non-locality. Recently Chen et. al. have proposed a more generalized Hardy-like argument and have shown that the probability of success increases with local system's dimension. Here we study the same in a minimally constrained theory, namely the generalized no-signaling theory(GNST). We find that not only the probability of success of this argument increases with local system dimension in GNST, it also takes a very simple functional form.
I argue that quantum mechanics is a realistic theory, but it violates either strong locality (no superluminal influences) or strict causality (diiferent effects cannot follow from the same cause).
We show that failure of local realism can be revealed to observers for whom only extremely coarse-grained measurements are available. In our instances, Bell's inequality is violated even up to the maximum limit while both the local measurements and the initial local states under scrutiny approach the classical limit. Furthermore, we can observe failure of local realism when an inequality enforced by non-local realistic theories is satisfied. This suggests that locality alone may be violated while realism cannot be excluded for specific observables and states. Small-scale experimental demonstra…
We investigate the violation of non-local realism using entangled coherent states (ECS) under nonlinear operations and homodyne measurements. We address recently proposed Leggett-type inequalities, including a class of optimized incompatibility ones and thoroughly assess the effects of detection inefficiency.
Local realism is in conflict with special quantum Bell-type models. Recently, several experiments have demonstrated violation of local realism if we trust their setup assuming special relativity valid. In this paper we question the assumption of relativity, point out not commented anomalies and show that the experiments have not closed objectivity loophole because clonability of the result has not been demonstrated. We propose several improvements in further experimental tests of local realism make the violation more convincing.
It is shown that a careful analysis of the `wrong' events (those not present in the usual formulations of the GHZ argument), which are a necessary feature of the tests of local realism involving independent sources, permits one to show that there is no local realistic model, which is capable to describe recent GHZ experiments performed in Innsbruck
We exhibit a local-hidden-variable model in agreement with the results of the two-photon coincidence experiment made by Torgerson et al. [Phys. Lett. A 204 (1995) 323]. The existence of any such model shows that the experiment does not exclude local realism.
The central focus of this work is to make progress towards understanding entanglement as a resource for computation by examining the quantum correlations that can be extracted from stabilizer states. As such, we focus on the stabilizer formalism, local realism, and the convergence of the two.
It is argued that local realism is a fundamental principle, which might be rejected only if experiments clearly show that it is untenable. A critical review is presented of the derivations of Bell's inequalities and the performed experiments, with the conclusion that no valid, loophole-free, test exists of local realism vs. quantum mechanics. It is pointed out that, without any essential modification, quantum mechanics might be compatible with local realism. This suggests that the principle may be respected by nature.
Quantum codewords are highly entangled combinations of two-state systems. The standard assumptions of local realism lead to logical contradictions similar to those found by Bell, Kochen and Specker, Greenberger, Horne and Zeilinger, and Mermin. The new contradictions have some noteworthy features that did not appear in the older ones.
Following the theoretical suggestion of Ref. [1,2], we present experimental results addressed to test restricted families of local realistic models, but without relying on the fair sampling assumption.
I make some critical comments on the article "An experimental test of non-local realism", by S. Groblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Zukowski, M. Aspelmeyer, & A. Zeilinger, Nature 446, p. 871-875 (2007). This article makes incorrect claims concerning Bell's theorem. Moreover, I point to the fact that a hypothesis referred to as "realism" in the article (Groblacher et al.) is not used in the deduction of Leggett's inequality.
We present a linear program that is capable of determining whether a set of correlations can be captured by a local realistic model. If the correlations can be described by such a model, the linear program outputs a joint probability distribution that produces the given correlations. If the correlations cannot be described under the assumption of local realism, the program outputs a Bell inequality violated by the correlations.
We show that it is, in principle, possible to perform local realism violating experiments of the Hardy type in which only position and momentum measurements are made on two particles emanating from a common source. In the optical domain, homodyne detection of the in-phase and out-of-phase amplitude components of an electromagnetic field is analogous to position and momentum measurement. Hence, local realism violations of the Hardy type are possible in optical systems employing only homodyne detection.
A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems, and these comprise a long list that includes the Kochen-Specker and Bell theorems, as well as elegant refinements by Mermin, Peres, Hardy, GHZ, and many others. Typically entanglement or carefully prepared multipartite systems have been considered essential for violations of local realism and for understanding quantum nonlocality. Here we show, to the contrar…
It is shown that the model introduced by Cabello et al. to criticize the Franson experiment suffers from the same weakness as the previous model introduced by Aerts et al. with the same purpose. It is also shown why we can assume with confidence that the Franson experiment does violate local realism.
We develop and exploit a source of two-photon four-dimensional entanglement to report the first two-particle all-versus-nothing test of local realism with a linear optics setup, but without resorting to a non-contextuality ssumption. Our experimental results are in well agreement with quantum mechanics while in extreme contradiction with local realism. Potential applications of our experiment are briefly discussed.
In Kaszlikowski [Phys. Rev. Lett. {\bf 85}, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled $N$-dimensional ($3 \leq N$) quantum objects is stronger than for two maximally entangled qubits and grows with $N$. In this paper we present the analytical proof of this fact for N=3.
We put bounds on the minimum detection efficiency necessary to violate local realism in Bell experiments. These bounds depends of simple parameters like the number of measurement settings or the dimensionality of the entangled quantum state. We derive them by constructing explicit local-hidden variable models which reproduce the quantum correlations for sufficiently small detectors efficiency.
Recently various papers have proposed to test local realism (LR) by considering electroweak CP-violation parameters values in neutral pseudoscalar meson systems. Considering the large interest for a conclusive test of LR and the experimental accessibility to these tests, in this paper we critically consider these results showing how they, albeit very interesting, require anyway additional assumptions and therefore cannot be considered conclusive tests of LR.
We show all-versus-nothing proofs of Bell's theorem in the one-dimensional transverse-field Ising model, which is one of the most important exactly solvable models in the field of condensed matter physics. Since this model can be simulated with nuclear magnetic resonance, our work might lead to a fresh approach to experimental test of the Greenberger-Horne-Zeilinger contradiction between local realism and quantum mechanics.
Tests of local realism vs quantum mechanics based on Bell's inequality employ two entangled qubits. We investigate the general case of two entangled quNits, i.e. quantum systems defined in an N-dimensional Hilbert space. Via a numerical linear optimization method we show that violations of local realism are stronger for two maximally entangled quNits (N=3,4,...,9), than for two qubits and that they increase with N. The two quNit measurements can be experimentally realized using entangled photons and unbiased multiport beamsplitters.
We show using a numerical approach that gives necessary and sufficient conditions for the existence of local realism, that the bound entangled state presented in Bennett et. al. Phys. Rev. Lett. 82, 5385 (1999) admits a local and realistic description. We also find the lowest possible amount of some appropriate entangled state that must be ad-mixed to the bound entangled state so that the resulting density operator has no local and realistic description and as such can be useful in quantum communication and quantum computation.
Are Bell's conditions for local realism general enough?
本文重新审视贝尔局域现实条件，提出更现实的物理条件以实现违反贝尔不等式的光学实验模型。
Fundamental principle of classical physics -- local realism, means that freely chosen observations can be explained by a local (slower than light) real process. It is apparently violated in quantum mechanics as shown by Bell theorem. Despite extreme efforts experiments have not conclusively confirmed this violation due to loopholes. We propose a new postulate that the description of quantum processes must be consistent with local realism, It also assumes existence of many worlds/copies of the same system, interacting weakly microscopically but strongly macroscopically, whose number can be esti…
We examine the prevalent use of the phrase ``local realism'' in the context of Bell's Theorem and associated experiments, with a focus on the question: what exactly is the `realism' in `local realism' supposed to mean? Carefully surveying several possible meanings, we argue that all of them are flawed in one way or another as attempts to point out a second premise (in addition to locality) on which the Bell inequalities rest, and (hence) which might be rejected in the face of empirical data violating the inequalities. We thus suggest that the phrase `local realism' should be banned from future…
Employing a procedure called monitoring---via a completely positive trace-preserving map that is able to interpolate between weak and projective measurements---we investigate the resilience of the recently proposed realism-based nonlocality to local and bilocal weak measurements. This analysis indicates realism-based nonlocality as the most ubiquitous and persistent form of quantumness within a wide class of quantum-correlation quantifiers. In particular, we show that the set of states possessing this type of quantumness forms a strict superset of symmetrically discordant states and, therefore…
Mermin's observation [Phys. Rev. Lett. {\bf 65}, 1838 (1990)] that the magnitude of the violation of local realism, defined as the ratio between the quantum prediction and the classical bound, can grow exponentially with the size of the system is demonstrated using two-photon hyper-entangled states entangled in polarization and path degrees of freedom, and local measurements of polarization and path simultaneously.
We show that quantum mechanics predicts an Einstein-Podolsky-Rosen paradox (EPR), and also a contradiction with local hidden variable theories, for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new, very strong premise, called macroscopic local realism. We link this premise to the Schrodinger-cat paradox. Our proposed experiments ensure all fields incident on each measurement apparatus are macroscopic. We show that an…
Theory-Independent Realism
本研究将量子力学语境下的实在论判据拓展至独立于理论的广义概率理论框架，基于测量概率、鲁棒性与Kullback-Leibler散度提出通用实在性量化指标，并在量子力学中验证其与已有非实在性测度的关联。
Ontological theories of quantum mechanics provide a realistic description of single systems by means of well-defined quantities conditioning the measurement outcomes. In order to be complete, they should also fulfil the minimal condition of macroscopic realism. Under the assumption of outcome determinism and for Hilbert space dimension greater than two, they were all proved to be contextual for projective measurements. In the recent years a generalized concept of non-contextuality was introduced that applies also to the case of outcome indeterminism and unsharp measurements. It was pointed out…
The usual entanglement swapping protocol can entangle two particles that never interact. Here we demonstrate an all-versus-nothing violation of local realism for a partial entanglement swapping process. A Clauser-Horne-Shimony-Holt-type inequality for two particles entangled by entanglement swapping is proposed for a practical experiment and can be violated quantum mechanically up to 4 beyond Cirel'son's bound 2sqr(2). Our result uncovers the intriguing nonlocal character of entanglement swapping and may lead to a conclusive (loophole-free) test of local realism versus quantum mechanics. The e…
An ensemble consisting on systems of two entangled spin 1/2 particles, all of them in the same global quantum state, are considered. The two spins are measured, each of them, on a fixed direction, at two randomly selected measurement times. Realism, plus locality and freedom of choice referred to these chosen times, are assumed. Then, from the sole correlation function related to the two measurements, without considering any Bell inequalities, a contradiction between these assumptions and quantum mechanics is found.
The concept of realism in quantum mechanics means that results of measurement are caused by physical variables, hidden or observable. Local hidden variables were proved unable to explain results of measurements on entangled particles tested far away from one another. Then, some physicists embraced the idea of nonlocal hidden variables. The present article proves that this idea is problematic, that it runs into an impasse vis-à-vis the special relativity.
A review and reformulation of macroscopic realism: resolving its deficiencies using the framework of generalized probabilistic theories
本文批判性回顾了宏观实在论及其测试存在的问题，提出在广义概率理论框架内重构宏观实在论，即当且仅当理论用严格经典的广义概率理论描述宏观系统时才为宏观实在论，从而为研究宏观实在论提供了新工具与新测试。
We report a local hidden-variable model which reproduces quantum predictions for the two-photon interferometric experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)]. The model works for the ideal case of full visibility and perfect detection efficiency. This result changes the interpretation of a series of experiments performed in the current decade.
We show that EPR's criterion of reality leads to contradictions in quantum mechanics. When locality is assumed, an inequality involving only one particle is violated, while when parameter and outcome dependence are assumed, EPR-realism is shown to be not Lorentz invariant. Quantum mechanics is both non-local and non-realistic.
A sequence of Bell inequalities for N-particle systems, which involve three settings of each of the local measuring apparatuses, is derived. For Greenberger-Horne-Zeilinger states, quantum mechanics violates these inequalities by factors exponentially growing with N. The threshold visibilities of the multiparticle sinusoidal interference fringes, for which local realistic theories are ruled out, decrease as (2/3)^N.
We show that for macroscopic measurements which cannot reveal full information about microscopic states of the system, the monogamy of Bell inequality violations present in quantum mechanics implies that practically all correlations between macroscopic measurements can be described by local realistic models. Our results hold for sharp measurement and arbitrary closed quantum systems.
Objections to the use of inequalities to address foundational issues are considered and shown to be invalid. The Clauser-Horne (CH) inequality is considered and interpreted in this light. It is shown that, applied correctly, the CH inequality can validly test aspects of locality. This paper establishes a firm methodological ground for a following paper analyzing a recent CH experiment.
We investigate the influence of environmental noise on polarization entangled light generated by parametric emission in a cavity. By adopting a recently developed separability criterion, we show that: i) self-stimulation may suppress the detrimental influence of noise on entanglement; ii) when self-stimulation becomes effective, a classical model of parametric emission incorporating noise provides the same results of quantum theory for the expectation values involved in the separability criterion. Moreover we show that, in the macroscopic limit, it is impossible to observe violations of local …
We investigate the nonlocal property of the fractional statistics in Kitaev's toric code model. To this end, we construct the Greenberger-Horne-Zeilinger paradox which builds a direct conflict between the statistics and local realism. It turns out that the fractional statistics in the model is purely a quantum effect and independent of any classical theory.We also discuss a feasible experimental scheme using anyonic interferometry to test this contradiction.
Most working scientists hold fast to the concept of 'realism' - a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenabl…
Loophole-free Bell inequality violations cannot disprove local realism
该研究指出贝尔不等式推导中误将局域实在论的充分条件当作必要条件，通过构建三个违反贝尔不等式的局域实在论模型，证明无漏洞的贝尔不等式违反也无法证伪局域实在论。
A simple proof of a key inequality required by the paper's analysis is presented. An introductory section discussing the paper's setup may be helpful to some readers. An alternative statistical analysis is suggested.
We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for test of realism not only in quantum mechanical systems, but also in quantum field systems. Also we propose a mathematically consistent derivation of the Leggett--Garg inequality in Wigner form, which was recently presented in the literature, for three and $n$ distinct moments of time. Contrary to these works, our rigor derivation uses…
We introduce a two-observer all-versus-nothing proof of Bell's theorem which reduces the number of required quantum predictions from 9 [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001); Z.-B. Chen et al., Phys. Rev. Lett. 90, 160408 (2003)] to 4, provides a greater amount of evidence against local realism, reduces the detection efficiency requirements for a conclusive experimental test of Bell's theorem, and leads to a Bell's inequality which resembles Mermin's inequality for three observers [N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990)] but requires only two observers.
It is briefly demonstrated that Gisin's so-called 'locality' assumption [arXiv:0901.4255] is in fact equivalent to the existence of a local deterministic model. Thus, despite Gisin's suggestions to the contrary, 'local realism' in the sense of Bell is built into his argument from the very beginning. His 'locality' assumption may more appropriately be labelled 'separability'. It is further noted that the increasingly popular term 'quantum nonlocality' is not only misleading, but tends to obscure the important distinction between no-signalling and separability. In particular, 'local non-realism'…
The two-photon interferometric experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a "Bell test of local realism". However, it has been suggested that this is incorrect due to the 50% postselection performed even in the ideal gedanken version of the experiment. Here we present a simple local hidden variable model of the experiment that successfully explains the results obtained in usual realizations of the experiment, even with perfect detectors. Furthermore, we also show that there is no such model if the switching of the local phase settings is done at a rat…
We consider relations between communication complexity problems and detecting correlations (violating local realism) with no local hidden variable model. We show first universal equivalence between characteristics of protocols used in that type of problems and non-signaling correlations. We construct non linear bipartite Bell type inequalities and strong nonlocality test with binary observables by providing general method of Bell inequalities construction and showing that existence of gap between quantum and classical complexity leads to violation of these inequalities. We obtain, first to our…
Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2 correlations. This new constraint rules out such models even in some situations in which standard Bell inequalities allow for explicit construction of such models. The whole analysis is performed without any additional assumptions on the form of local realistic models.
Based on the form invariance of the structures given by Khinchin's axiomatic foundations of information theory and the pseudoadditivity of the Tsallis entropy indexed by q, the concept of conditional entropy is generalized to the case of nonadditive (nonextensive) composite systems. The proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context, indicating its utility for characterizing quantum entanglement. A criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipa…
We investigate the violation of Leggett's inequality for non-local realism using entangled coherent states and various types of local measurements. We prove mathematically the relation between the violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when tested by the same resources. For Leggett inequalities, we generalize the non-local realistic bound to systems in Hilbert spaces larger than bidimensional ones and introduce an optimization technique that allows to achieve larger degrees of violation by adjusting the local measurement settings. Our work descr…
I point out critical errors in the paper "Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space" by J. Christian, published in IEEE Access. Christian's paper in fact contains several conflicting models. None of them form counterexamples to Bell's theorem. Most of Christian's paper is devoted to a model based on the detection loophole due to Pearle (1970).
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