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arXiv:1303.5124 · Physical Review A

Physics of crypto-nonlocality

Miguel Navascués

Published Feb 18, 2014• 1 citation
arXivHTMLPDF

Abstract

In 2003, Leggett introduced his model of crypto-nonlocality based on considerations on the reality of photon polarization [A. J. Leggett, Found. Phys. 33, 1469 (2003)]. In this paper, we prove that, contrary to hints in subsequent literature, crypto-nonlocality does not follow naturally from the postulate that polarization is a realistic variable. More explicitly, consider physical theories where (a) faster-than-light communication is impossible, (b) all physical photon states have a definite polarization, and (c) given two separate photons, if we measure one of them and post-select on the result, the measurement statistics of the remaining system correspond to a photon state. We show that the outcomes of any two-photon polarization experiment in these theories must follow the statistics generated by measuring a separable two-qubit quantum state. Consequently, in such experiments any instance of entanglement detection---and not necessarily a Leggett inequality violation---can be regarded as a refutation of this class of theories.

DOI
10.1103/physreva.89.022114

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In 2003, Leggett introduced his model of crypto-nonlocality based on considerations on the reality of photon polarization [A. J. Leggett, Found. Phys. 33, 1469 (2003)]. In this paper, we prove that, contrary to hints in subsequent literature, crypto-nonlocality does not follow naturally from the postulate that polarization is a realistic variable. More explicitly, consider physical theories where (a) faster-than-light communication is impossible, (b) all physical photon states have a definite polarization, and (c) given two separate photons, if we measure one of them and post-select on the result, the measurement statistics of the remaining system correspond to a photon state. We show that the outcomes of any two-photon polarization experiment in these theories must follow the statistics generated by measuring a separable two-qubit quantum state. Consequently, in such experiments any instance of entanglement detection---and not necessarily a Leggett inequality violation---can be regarded as a refutation of this class of theories.
Abstract It has been well established that quantum mechanics (QM) violates Bell inequalities (BI), which are consequences of local realism (LR). Remarkably QM also violates Leggett inequalities (LI), which are consequences of a class of nonlocal realism called crypto-nonlocal realism (CNR). Both LR and CNR assume that measurement outcomes are determined by preexisting objective properties, as well as hidden variables (HV) not considered in QM. We extend CNR and LI to include the case that the measurement settings are not externally fixed, but determined by HV. We derive a new version of LI, which is then shown to be violated by entangled BdB_dBd​ B d mesons, if charge–conjugation–parity (CP) symmetry is indirectly violated, as indeed established. The experimental result is quantitatively estimated by using the indirect CP violation parameters, and the maximum of a suitably defined relative violation is about 2.7%2.7\%2.7% 2.7 % . Our work implies that particle physics violates CNR. Our LI can also be tested in other systems such as photon polarizations.
According to Bell's theorem, any model based on local variables cannot reproduce certain quantum correlations. A critical question is whether one could devise an alternative framework, based on nonlocal variables, to reproduce quantum correlations while adhering to fundamental principles. Leggett proposed a nonlocal model, termed crypto-nonlocality, rooted in considerations of the reality of photon polarization, but this property restricted it to being bi-dimensional. In this Letter, we extend the crypto-nonlocal model to higher dimensions and develop a framework for constructing experimentally testable Leggett-type inequalities for arbitrary dimensions. Our investigation into models that yield specific predictions exceeding those of quantum mechanics is intriguing from an information-theoretic perspective and is expected to deepen our understanding of quantum correlations.
Nonlocal realism represents the last classical cornerstone in conflict with quantum theory, and has been shown to be largely untenable in bipartite systems [Nature 446, 871 (2007); Nature Physics 4, 681 (2008)]. We extend the Leggett-type nonlocal realistic model to arbitrary N-partite systems with polarizer settings, and derive rigorous inequalities that distinguish quantum predictions from nonlocal realistic theories. The derivation yields a fundamental double inequality that is universally valid, from which the Leggett-type bounds follow under specific measurement settings. As an illustration, we demonstrate quantum violations of these inequalities for Greenberger-Horne-Zeilinger (GHZ) states, with maximal violation 2(\sqrt{5}+1). Our results show that nonlocal realism in multipartite systems is experimentally testable.
Bell's inequality is widely regarded as the death knell of local hidden variable theories. However, this paper points out that Bell's argument implicitly relies on an overly narrow assumption about what constitutes a "local hidden variable"—namely, that hidden variables must assign measurement outcomes to each particle independently at the moment of measurement. This paper proposes that the deterministic correspondence established between entangled particles at the moment of their creation, and determined by initial conditions, can itself serve as a local hidden variable. As long as the polarization direction of the photons is not altered, this correspondence persists indefinitely. It is independent of whether a measurement is performed, and requires no superluminal communication to sustain. From this perspective, quantum entanglement experiments do not violate special relativity; the violation of Bell's inequality merely rules out a specific class of hidden variable models, not all forms of local realism.
Nonlocality as a fundamental aspect of quantum mechanics is witnessed by violation of Bell inequality or its variants, for which all relevant studies assume some correlations exhibited by local realistic theories. The strategy of Bell's theorem is to establish some criteria to distinguish local realistic theories from quantum mechanics with respect to the nonlocal nature of entangled systems. Here we propose a model independent study of nonlocality that needs not to assume any local theory since observation of the expected nonlocal effect is straightforward quantum mechanically. Our proposal involves a bipartite polarization-entangled system in which one photon immediately reduces into a circular-polarization (CP) state when its partner at a space-like distance is detected in another CP state. The state reduction of the photon can be mechanically monitored because a CP photon carries angular momentum and exerts a torque on a half-wave plate whose mechanical motion is measurable, which is well described by quantum mechanics and independent of any local realistic assumption.
"In 1935, Einstein, Podolsky, and Rosen questioned whether quantum mechanics can be complete, as it seemingly does not adhere to a natural view of reality: local realism, which is the notion that an event can only be influenced by events in the past lightcone, and can only influence events in the future lightcone. This question sparked a philosophical debate that lasted for three decades, until John Bell demonstrated that not only are quantum mechanics and local realism philosophically incompatible, but they predict different statistical results for an appropriate set of measurements on entangled particles, which changed the debate to a scientific discussion. Since then, Bell inequality violations have occurred in a plethora of systems, hinting that local realism is indeed wrong. However, every experiment had imperfections that complicated the interpretation --- the experiments had so-called ""loopholes"" which allowed local realism to persist. In this manuscript, we present our work in using optimized sources of entangled photons to perform the long-sought loophole-free Bell test. This landmark experiment invalidates local realism to the best that science will allow. Beyond answering questions on reality, these Bell tests have a important application in generating provably-secure private random numbers, which then can be used as a seed for cryptographic applications. Not only do we demonstrate that nonlocality must exist, but we begin an experimental exploration in an attempt to understand and quantify this nonlocality. We do so by considering all theories that obey no-signaling (or relativistic causality). In our experiments, we observe the counter-intuitive feature of measuring more nonlocality with less entangled states. We also place a bound on the predictive power of any theory that obeys relativistic causality. And finally, we are able to measure quantum correlations only attainable through complex qubits. This work merely begins to probe the quantum boundary, beginning a journey that may someday find evidence of a beyond-quantum theory."