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arXiv:quant-ph/0307114 · Physical Review A

Einstein-Podolsky-Rosen correlation in a gravitational field

Hiroaki Terashima, Masahito Ueda

Published Mar 31, 2004• 81 citations
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Abstract

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.

DOI
10.1103/physreva.69.032113

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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 formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction deteriorates in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing velocity of the observers if the directions of the measurement are fixed. However, this does not imply a breakdown of non-local correlation since the perfect anti-correlation is maintained in appropriately chosen different directions. When considering moving frames we must take account of this relativistic effect on the EPR correlation and on the violation of Bell's inequality for quantum communication.
Within the framework of relativistic quantum theory, we consider the Einstein-Podolsky-Rosen (EPR) gedanken-experiment in which measurements of the spin are performed by moving observers. We find that the perfect anti-correlation in the same direction between the EPR pair no longer holds in the observers' frame. This does not imply a breakdown of the non-local correlation. We explicitly show that the observers must measure the spin in appropriately chosen different directions in order to observe the perfect anti-correlation. This fact should be taken into account in utilizing the entangled state in quantum communication by moving observers.
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.
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.
For an Einstein–Podolsky–Rosen pair of spin-1/2 particles in circular orbits in a general axially symmetric spacetime, the spin precession angle is obtained. Hovering observers are introduced for ensuring fixed reference frames to perform suitable reliable measurements. Frame-dragging of spinning holes is explicitly incorporated relative to hovering observers. The spin-singlet state is found to be mixed with the spin-triplet by acceleration and gravity effects, which deteriorate the perfect anti-correlation of an entangled pair of spins measured by hovering observers. Finally, an algorithm to calculate spin precession for a general axially symmetric spacetime is proposed. This algorithm is applied to study the complete list of expanding and twisting Type-D Plebański–Demiański black holes and their descendent limiting solutions with lower parameters.