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arXiv:1105.1897 · Europhysics Letters (EPL)

Large-scale EPR correlation and gravitational waves backgrounds

Brahim Lamine, R. Hervé, Marc-Thierry Jaekel, Astrid Lambrecht, Serge Reynaud

Published Jun 30, 2011• 45 citations
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Abstract

We study how quantum correlations survive at large scales in spite of their exposition to stochastic backgrounds of gravitational waves. We consider Einstein-Podolski-Rosen (EPR) correlations built up on the polarizations of photon pairs and evaluate how they are affected by the cosmic gravitational wave background (CGWB). We evaluate the quantum decoherence of the EPR correlations in terms of a reduction of the violation of the Bell inequality as written by Clauser, Horne, Shimony and Holt (CHSH). We show that this decoherence remains small and that EPR correlations can in principle survive up to the largest cosmic scales.

DOI
10.1209/0295-5075/95/20004

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We study how quantum correlations survive at large scales in spite of their exposition to stochastic backgrounds of gravitational waves. We consider Einstein-Podolski-Rosen (EPR) correlations built up on the polarizations of photon pairs and evaluate how they are affected by the cosmic gravitational wave background (CGWB). We evaluate the quantum decoherence of the EPR correlations in terms of a reduction of the violation of the Bell inequality as written by Clauser, Horne, Shimony and Holt (CHSH). We show that this decoherence remains small and that EPR correlations can in principle survive up to the largest cosmic scales.
For quantum communication in a gravitational field, the properties of the Einstein-Podolsky-Rosen (EPR) correlation are studied within the framework of general relativity. Acceleration and gravity are shown to deteriorate the perfect anticorrelation of an EPR pair of spins in the same direction, and apparently decrease the degree of the violation of Bell's inequality. To maintain the perfect EPR correlation and the maximal violation of Bell's inequality, observers must measure the spins in appropriately chosen different directions which depend on the velocity of the particles, the curvature of the space-time, and the positions of the observers. Near the event horizon of a black hole, the appropriate directions depend so sensitively on the positions of the observers that even a very small uncertainty in the identification of the observers' positions leads to a fatal error in quantum communication, unless the observers fall into the black hole together with the particles.
We study the Bell inequality in a holographic model of the casually disconnected Einstein–Podolsky–Rosen (EPR) pair. The Clauser–Horne–Shimony–Holt (CHSH) form of Bell inequality is constructed using holographic Schwinger–Keldysh (SK) correlators. We show that the manifestation of quantum correlation in Bell inequality can be holographically reproduced from the classical fluctuations of dual accelerating string in the bulk gravity. The violation of this holographic Bell inequality supports the essential quantum property of this holographic model of an EPR pair.
The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Sixty five years ago, the most significant paper questioning a fundamental aspect of quantum phenomena was written by Einstein, Podolsky and Rosen (EPR) [1]. They addressed the question whether the wave-function represented a complete description of reality in quantum mechanics, and argued that it didn’t. Bohr’s reply to this paper [2] was not sufficient to resolve the fundamental issues raised by EPR. Decades later, Bohm rephrased the EPR problem [3] in terms of particles correlated in their spin and this helped enormously in analyzing the problem with clarity. John Bell analyzed the EPR problem in the early sixties and established the Bell’s inequalities obeyed by
The Einstein-Podolsky-Rosen (EPR) paradox challenges the completeness of quantum mechanics under the assumptions of separability and locality, while Bell's theorem and its loophole-free experimental confirmations rule out local hidden variables and establish that entangled correlations are nonlocal yet no-signaling. This paper formulates, within the spacetime-quantum unified-field theory, a self-contained resolution of the paradox. Starting from the six axioms of the theory, we model the entangled pair as two local excitations of the single global spacetime-quantum field, a coherent superposition of discrete spacetime quanta (Axiom 1). We show that the EPR elements of reality are not attributes of the separated subsystems but properties of the global coherent configuration established within the common past light cone, so that EPR's tacit separability premise fails in this ontology (Axioms 1 and 5). Measurement is identified as a strictly local energy exchange (Axioms 2 and 5) whose influence propagates at most at the speed of light by the local hyperbolic master equation (Axiom 3), and we prove, by the invariance of the reduced density matrix, that no signaling is possible. The Bell correlations are reproduced as a consistency condition inherited from the standard-model sector (Axiom 4), with the Tsirelson bound 2√2 following from the no-signaling structure. Complete derivations of the correlation function, the Clauser-Horne-Shimony-Holt inequality and its violation, the no-signaling theorem, the local measurement model, and the coherence-entanglement relation are provided in the appendices.
An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment that can actually be performed with present technology to test local realism. Quantum mechanics violates this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities [for example, those of J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969); S. J. Freedman and I. F. Clauser ibid. 28, 938 (1972); and J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974)] by a factor of 2.\sqrt{2}.2​. Thus the magnitude of violation of the inequality derived in this paper is approximately 20.7% larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.
We examine the properties and behavior of the original Einstein-Podolsky-Rosen (EPR) wave function [Phys. Rev. 47, 777 (1935)] and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell [Ann. (N.Y.) Acad. Sci. 480, 263 (1986)] based on the Wigner phase-space distribution [Phys. Rev. 40, 749 (1932)], which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell's analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.