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

Journal Article · Fri Jul 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.012307· OSTI ID:20718315

Schliemann, John ^[1]

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1. Department of Physics and Astronomy, University of Basel, CH-4056 Basel (Switzerland)

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} is entirely determined by the diagonal elements of {rho} 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} 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.

• OSTI ID: 20718315
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
COMPARATIVE EVALUATIONS
DENSITY MATRIX
EIGENVALUES
ENERGY LEVELS
QUANTIZATION
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
SPIN
SU-2 GROUPS
SUM RULES
TENSORS
TRANSFORMATIONS