Entanglement properties of a two spin-one particle system under a Lorentz transformation

TL;DR

This paper investigates how entanglement in a two spin-one particle system behaves under Lorentz transformations, identifying states with invariant entanglement and analyzing implications for quantum information.

Contribution

It introduces a complete set of spin states with zero entanglement change under Lorentz boosts and explicitly constructs maximally entangled invariant states.

Findings

Entanglement in certain states remains unchanged under Lorentz transformations.

Maximally entangled invariant states are explicitly constructed.

Particle-particle entanglement is Lorentz invariant, ensuring quantum correlation consistency.

Abstract

We analize the entanglement change, under a Lorentz transformation, of a system consisting of two spin-one particles, considering different partitions of the Hilbert space, which has spin and momentum degrees of freedom. We show that there exists a complete set of states of the spin subspace in which the entanglement change of any state in the set is zero for all partitions and all values of the Wigner angle. Moreover, these states only change by a global phase factor under the Lorentz boost. Within this basis, maximally entangled invariant states, interesting for quantum information purposes, are explicitly obtained. On the other hand, the entanglement in the particle- particle partition is Lorentz invariant, thus protecting the consistency of quantum correlations and teleportation results. We show how our results may be generalized to arbitrary spin.