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arXiv:quant-ph/0204138 · Quantum Information and Computation

Einstein-Podolsky-Rosen correlation seen from moving observers

Hiroaki Terashima, Masahito Ueda

Published May 1, 2003• 47 citations
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Abstract

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.

DOI
10.26421/qic3.3-4

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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 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.
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.
Abstract The Einstein‐Podolsky‐Rosen “gedanken‐experiment” does not imply non‐local interactions or an “action‐at‐a‐distance”. Contrary, the EPR proves the measurements at one particle does not have influences at canonical variables of the other particles if the quantum‐mechanical commutation relations are true. But, the EPR implices correlations between the particles which come in by “subjective knowledge”. These correlations are a priori informations about the relative motion or, complementarily, about the motion of the center of mass. The impression of an action‐at‐a‐distance is produced by the use of usual particle coordinates in the EPR‐arrangements. The discussion of the Einstein‐Podolsky‐Rosen “gedanken‐experiment” (EPR) has been going on over fifty years. EINSTEIN, PODOLSKY, and ROSEN formulated their famous paradox in 1935, and in the discussion between N. BOHR (1935, 1949) and A. EINSTEIN (1936, 1948); A. EINSTEIN (1948) made his point that the EPR implied an “action‐at‐a‐distance” for quantum‐mechanical particles (without obvious classical interactions). His argument is the starting point for the recent discussion about EPR and causality (see A. Aspect, 1981).
Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.