Is bound entanglement Lorentz invariant?

TL;DR

This paper investigates whether bound entanglement remains invariant under Lorentz transformations, revealing that relativistic boosts can alter the entanglement classification of quantum states.

Contribution

It demonstrates that Lorentz boosts can change the entanglement classification of bound states, challenging the assumption of Lorentz invariance in entanglement properties.

Findings

Boosted observers may see different entanglement types in the same state.

Bound entanglement classification is not Lorentz invariant.

Entanglement measures are difficult to define universally under relativistic transformations.

Abstract

Bound entanglement, in contrast to free entanglement, cannot be distilled into maximally entangled states by two local observers applying measurements and utilizing classical communication. In this paper we ask whether a relativistic observer classifies states according to being separable, bound or free entangled in the same manner as an unboosted observer. Surprisingly, this turns out not to be the case. And that even if the system in a given inertial frame of reference is separable with respect to the partition momenta versus spins. In detail, we show that if the spin state is initially bound entangled, some boosted observers observe their spin states to be either bound entangled, separable or free entangled. This also explains why a general measure of the entanglement property is difficult to find.