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arXiv:2003.03641 · The European Physical Journal Plus

Lorentz invariant quantum concurrence for $$\textit{SU}(2) \otimes \textit{SU}(2)$$ spin–parity states

Alex E. Bernardini, Victor A. S. V. Bittencourt, Massimo Blasone A

Published Mar 1, 2020• 5 citations
arXivHTMLPDF
DOI
10.1140/epjp/s13360-020-00323-w

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Lorentz invariant quantum concurrence for SU(2)⊗SU(2)\textit{SU}(2) \otimes \textit{SU}(2)SU(2)⊗SU(2) spin–parity states
We consider two spacelike separated Dirac particles and construct five invariants under the spinor representations of the local proper orthochronous Lorentz groups. All of the constructed Lorentz invariants are identically zero for product states. The behavior of the Lorentz invariants under local unitary evolutions that act unitarily on any subspace with fixed particle momenta is studied. All of the Lorentz invariants have invariant absolute values on such subspaces if the evolutions are generated by local zero-mass Dirac Hamiltonians. Some of them also for the case of nonzero mass. Therefore, they are considered potential candidates for describing spinor entanglement of two Dirac particles, with either zero or arbitrary mass. Furthermore, their relations to the Wootters concurrence is investigated and their representations in the Foldy-Wouthuysen picture is given.
Super-quantum correlation for SU(2) invariant state in 4⊗24\otimes 24⊗2 4 ⊗ 2 system