Spin entanglement of two spin-1/2 particles in a classical gravitational field

TL;DR

This paper investigates how a classical gravitational field influences the spin entanglement of two spin-1/2 particles, showing conditions under which entanglement remains invariant or diminishes due to spacetime curvature effects.

Contribution

It introduces a detailed analysis of spin entanglement dynamics in curved spacetime, highlighting the impact of Wigner rotations caused by gravity on quantum entanglement.

Findings

Entanglement can remain invariant along specific paths in a gravitational field.

Increasing angular velocity or proper time reduces the spin entanglement.

Wigner rotations caused by gravity influence the evolution of quantum entanglement.

Abstract

The effect of a classical gravitational field on the spin entanglement of a system of two spin-1/2 particles moving in the curved spacetime is discussed. The system is described by a two-particle Gaussian wave packet represented in the momentum space and both the acceleration of the system and the curvature of the spacetime cause to produce a Wigner rotation acting on the wave packet as it moves along a path in the curved spacetime. By calculating the reduced density operator at a final point, we focus on the spin entanglement of the system. In a spherically symmetric and static gravitational field, for example a charged black hole, there can be particular paths on which the Wigner rotation is trivial and so the initial reduced density matrix remains intact. This causes the spin entanglement to be invariant during the motion. The spin entanglement descends to zero by increasing the angular velocity of the mean centroid of the system as well increasing the proper time during which the centroid moves on its circular path around the center.