On Relativistic Quantum Information Properties of Entangled Wave Vectors of Massive Fermions

TL;DR

This paper investigates how special relativity affects entanglement between spins and momenta of massive fermions, revealing that entanglement is not Lorentz invariant and varies with reference frames, with no compensation between degrees of freedom.

Contribution

It provides a detailed analysis of relativistic effects on entanglement in massive fermions, highlighting the non-invariance and differential changes in spin and momentum entanglements.

Findings

Spin and momentum entanglements decrease under Lorentz transformations.

No entanglement compensation occurs between spin and momentum.

Entanglement change rates are monotonic and depend on particle distinguishability.

Abstract

We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin-1/2 massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative motion. For the case of indistinguishable particles, we consider a balanced scenario where the momenta of the pair are well-defined but not maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ($\eta$) family of entangled bipartite states. For the case of distinguishable particles, we consider an unbalanced scenario where the momenta of the pair are well-defined and maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ($\xi$) family of non-maximally entangled bipartite states. In both cases, we show that neither the spin-spin ($ss$) nor the momentum-momentum ($mm$) entanglements quantified by means of Wootters' concurrence are Lorentz invariant quantities: the total amount of entanglement regarded as the sum of these entanglements is not the same in different inertial moving frames. In particular, for any value of the entangling parameters, both $ss$ and $mm$-entanglements are attenuated by Lorentz transformations and their parametric rates of change with respect to the entanglements observed in a rest frame have the same monotonic behavior. However, for indistinguishable (distinguishable) particles, the change in entanglement for the momenta is (is not) the same as the change in entanglement for spins. As a consequence, in both cases, no entanglement compensation between spin and momentum degrees of freedom occurs.