Fidelity for States of Two Spin- $\frac{1}{2}$ Particles in Moving Frames

Abstract

Fidelity for the spin part of states of two spin- \(\frac{1}{2}\) particles is investigated from the viewpoint of moving observers. Using a numerical approach, the behavior of the fidelity in terms of the boost parameter is described for different amounts of spin entanglement and momentum entanglement. It is shown that for the spin entangled states the fidelity decreases less than that of the case of spin product states and there are special cases for which the fidelity remains perfect regardless of moving observers’ velocity. Generally, in the limit of boosts with speeds close to the speed of light, the fidelity saturates, i.e., it reaches to a constant value that depends on the amount of momentum entanglement and the width of the momentum distribution function.