Relativistic entanglement of two massive particles

TL;DR

This paper analyzes how relativistic effects, specifically Lorentz boosts and Wigner rotations, influence the entanglement of two massive spin-1/2 particles across different partitions and observers, revealing frame-dependent entanglement changes.

Contribution

It systematically investigates the impact of Lorentz transformations on entanglement and Bell inequality violations in a two-particle relativistic quantum system.

Findings

Entanglement varies with inertial frame for certain partitions.

Wigner rotations entangle spin and momentum states.

Bell inequality violations can be maximized for any observer.

Abstract

We describe the spin and momentum degrees of freedom of a system of two massive spin--$\tfrac{1}{2}$ particles as a 4 qubit system. Then we explicitly show how the entanglement changes between different partitions of the qubits, when considered by different inertial observers. Although the two particle entanglement corresponding to a partition into Alice's and Bob's subsystems is, as often stated in the literature, invariant under Lorentz boosts, the entanglement with respect to other partitions of the Hilbert space on the other hand, is not. It certainly does depend on the chosen inertial frame and on the initial state considered. The change of entanglement arises, because a Lorentz boost on the momenta of the particles causes a Wigner rotation of the spin, which in certain cases entangles the spin- with the momentum states. We systematically investigate the situation for different classes of initial spin states and different partitions of the 4 qubit space. Furthermore, we study the behavior of Bell inequalities for different observers and demonstrate how the maximally possible degree of violation, using the Pauli-Lubanski spin observable, can be recovered by any inertial observer.