Entanglement of zero angular momentum mixtures and black hole entropy

Abstract

We calculate the entanglement of formation and the entanglement of distillation for arbitrary mixtures of the zero spin states on an arbitrary-dimensional bipartite Hilbert space. Such states are relevant to quantum black holes and to decoherence-free subspaces based communication. The two measures of entanglement are equal and scale logarithmically with the system size. We discuss its relation to the black hole entropy law. Moreover, these states are locally distinguishable but not locally orthogonal, thus violating a conjecture that the entanglement measures coincide only on locally orthogonal states. We propose a slightly weaker form of this conjecture. Finally, we generalize our entanglement analysis to any unitary group.

5 pages, revtex4 Final version. A discussion of local orthogonality and entanglement is added

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• Many-body singlets by dynamic spin polarization
• From Entanglement Witness to Generalized Catalan Numbers
• Quantum information in loop quantum gravity
• Entanglement cost hierarchies in quantum fragmented mixed states