Einstein-Podolsky-Rosen correlation in gravitational field

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.