Fidelity of two-particle wave packets moving around a schwartzchid spacetime

Fidelity for two-particle wave packets moving around a schwartzchid spacetime is discussed.Both acceleration and gravity cause to produce a wigner rotation that transforms a wave packet as it moves along a specified path in the gravitational feild .It is shown that for fixed elapsed proper time and angular momentum of the centroid , there always exist one circular orbit on which the spin fidelity is minimum.