Global Dirac bispinor entanglement under Lorentz boosts. (arXiv:1801.00758v1 [quant-ph])

We consider the effects of Lorentz boosts on the quantum entanglement encoded
by a pair of massive spin $\frac{1}{2}$ particles properly described by Dirac
bispinors. Such a system incorporates four degrees of freedom -- related to the
intrinsic parity and to the spin of a pair of Dirac particles. Because its
natural multipartite structure, the Meyer-Wallach global measure of
entanglement is preliminarily used for computing global quantum correlations
while entanglement encoded only by spin degrees of freedom is measured through
the negativity of the reduced spin-spin state. We develop a general framework
to compute the changes on quantum entanglement induced by a boost, and then
specialize the formalism to describe three particular anti-symmetric states. We
find that, for instance, spin-spin entanglement cannot be created by the action
of a Lorentz boost in a spin-spin separable anti-symmetric state. On the other
hand, maximal spin-spin entanglement encoded by anti-symmetric superpositions
is degraded by boosts driven by high-speed frame transformations. Finally, we
also consider the effects of boosts in chiral states, which exhibit interesting
invariance properties.

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