Entanglement of two relativistic particles with discrete momenta

TL;DR

This paper investigates how Lorentz boosts affect the entanglement of two relativistic spin-1/2 particles with discrete momenta, revealing complex behaviors and providing insights into relativistic quantum systems.

Contribution

It systematically analyzes the impact of Lorentz boosts on bipartite spin entanglement with discrete momenta, using Werner states and various boost scenarios.

Findings

Lorentz boosts induce non-trivial changes in bipartite spin entanglement.

Visualization helps explain the evolution of spin state concurrence.

The model offers insights applicable to systems with continuous momenta.

Abstract

We study the structure of maps that Lorentz boosts induce on the spin degree of freedom of a system consisting of two massive spin-$1/2$ particles. We consider the case where the spin state is described by the Werner state and the momenta are discrete. Transformations on the spins are systematically investigated in various boost scenarios by calculating the orbit and concurrence of the bipartite spin state with different kinds of product and entangled momenta. We confirm the general conclusion that Lorentz boosts cause non-trivial behavior of bipartite spin entanglement. Visualization of the evolution of the spin state is shown to be valuable in explaining the pattern of concurrence. The idealized model provides a basis of explanation in terms of which phenomena in systems involving continuous momenta can be understood.