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Quantum Information Processing

Super-quantum correlation for SU(2) invariant state in $$4\otimes 2$$ 4 ⊗ 2 system

Linsong Li, Yuan-Hong Tao, Hua Nan, Hui Xu

Published Feb 27, 2018• 3 citations
Publisher
DOI
10.1007/s11128-017-1789-2

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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 study entanglement in mixed bipartite quantum states which are invariant under simultaneous SU(2) transformations in both subsystems. Previous results on the behavior of such states under partial transposition are substantially extended. The spectrum of the partial transpose of a given SU(2)-invariant density matrix rho\\rhorho is entirely determined by the diagonal elements of rho\\rhorho in a basis of tensor-product states of both spins with respect to a common quantization axis. We construct a set of operators which act as entanglement witnesses on SU(2)-invariant states. A sufficient criterion for rho\\rhorho having a negative partial transpose is derived in terms of a simple spin correlator. The same condition is a necessary criterion for the partial transpose to have the maximum number of negative eigenvalues. Moreover, we derive a series of sum rules which uniquely determine the eigenvalues of the partial transpose in terms of a system of linear equations. Finally we compare our findings with other entanglement criteria including the reduction criterion, the majorization criterion, and the recently proposed local uncertainty relations.