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.Comment: 22 pages, 3 figures, several minor revisions are mad