Fidelity for States of Spin- $\frac{1}{2}$ Particles Moving in a Traversable Wormhole Spacetime

Abstract

Fidelity for states of spin- \(\frac{1}{2}\) particles moving in a static spherically symmetric traversable wormhole spacetime is discussed. When the centroid of the corresponding wave packet moves along a specified path in the gravitational field, both acceleration and gravity cause to transform the state of the particle. For circular orbits of the centroid coinciding the throat of wormhole, the fidelity between initial and final states of the whole system as well as the fidelity of the spin parts of the states are equal to the unity. This means that, the error in quantum communication diminishes on such a 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. The fidelity for wave packets moving along a radial geodesic toward the throat of wormhole is also discussed. In this case, the centroid traverses the wormhole and reaches to the other side, with a perfect fidelity for the spin parts, though the fidelity for the states of the whole system is not perfect.