Fidelity of Two-particle Wave Packets Moving around the Schwarzschild Spacetime


Quantum information theory, that is, transmission, storage and processing of information using quantum mechanical system, is now well developed. Many novel features of this theory relay on the entanglement and the non-locality associated with it. It is important to study all those processes that might have an effect on quantum information. Recently, a number of papers have disscused how entanglement is affected y the Lorentz trasformation in the jargon of special relativity. Some efforts have been made to discuss the effect of gravitational field on quantum information. In this article we discuss fidelity between the initial and final states of a bipartite quantum system consisting of two spin-1/2 particles that are moving around the Schwarzschild spacetime. Both acceleration and gravity cause to produce a Wigner rotation that transforms the wave packet as it moves along a specified path in the gravitational field. For considered circular paths, the fidelity between the spin parts of initial and final states of the system, called the spin fidelity, is obtained as a function of angular velocity, elapsed proper time and radius of circular paths. For fixed elapsed proper time and angular momentum of the centroid, there always exists one circular orbit with determined radius on which the fidelity of spin parts is minimum. Using a numerical approach, the behavior of the spin fidelity in terms of the angular velocity, as well as the radius of paths is described for both the spin singlet and spin triplet states.