Optimal entanglement criterion for mixed quantum states

Abstract

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N >= 4. It is shown that Phi detects many entangled states with positive partial transposition (PPT) and that it leads to a class of optimal entanglement witnesses. This implies that there are no other witnesses which can detect more entangled PPT states. The map Phi yields a systematic method for the explicit construction of high-dimensional manifolds of bound entangled states.

4 pages, no figures, replaced by published version (minor changes), Journal-reference added

References in corpus (4)

• Concurrence of arbitrary dimensional bipartite quantum states
• Entanglement in SO(3)-invariant bipartite quantum systems
• Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
• State space structure and entanglement of rotationally invariant spin systems

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• The geometry of bipartite qutrits including bound entanglement
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• A class of positive atomic maps
• Separability, entanglement and full families of commuting normal matrices
• Maximum Entanglement in Squeezed Boson and Fermion States
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• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• Positive maps, majorization, entropic inequalities, and detection of entanglement
• Constrained bounds on measures of entanglement
• Beyond the standard entropic inequalities: stronger scalar separability criteria and their applications
• Relative entropy of entanglement of rotationally invariant states
• A general scheme for construction of scalar separability criteria from positive maps
• Entanglement of positive definite functions on compact groups
• Extended Reduction Criterion and Lattice States