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arXiv quant-ph/0307114quant-ph
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引力场中的Einstein-Podolsky-Rosen关联

Einstein-Podolsky-Rosen correlation in gravitational field

Hiroaki Terashima, Masahito Ueda

摘要:

在广义相对论的框架下,研究了引力场中量子通信的Einstein-Podolsky-Rosen(EPR)关联的性质.加速度和引力的存在使同向EPR自旋对的完美反关联变差,并明显降低了Bell不等式的违反程度。为了保持完美的EPR相关性和贝尔不等式的最大违反,观测者必须在适当选择的不同方向上测量自旋。哪个方向是合适的取决于粒子的速度、时空的曲率和观测者的位置。在黑洞的事件视界附近,适当的方向非常敏感地依赖于观察者的位置,以至于在确定观察者位置时,即使非常小的不确定性也会导致量子通信中的致命错误,除非观察者与粒子一起落入黑洞。

英文摘要:

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 anti-correlation 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 directions are appropriate depends on the velocity of the particles, the curvature of the spacetime, 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.

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