Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others

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dc.creatorSchliemann, John
dc.date2005-03-14
dc.date2005-05-15
dc.date.accessioned2026-07-07T06:12:23Z
dc.date.available2026-07-07T06:12:23Z
dc.descriptionWe 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 $ρ$ is entirely determined by the diagonal elements of $ρ$ 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 $ρ$ 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.
dc.description7 pages, no figures, version to appear in Phys. Rev. A
dc.identifierhttps://arxiv.org/abs/quant-ph/0503123
dc.identifierhttp://arxiv.org/abs/quant-ph/0503123
dc.identifierPhys. Rev. A 72, 012307 (2005)
dc.identifierdoi:10.1103/PhysRevA.72.012307
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/92770
dc.subjectQuantum Physics
dc.subjectStatistical Mechanics
dc.titleEntanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
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