Generic local distinguishability and completely entangled subspaces

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Walgate, Jonathan
Scott, Andrew
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Murray T Batchelor (Editor-in-Chief)

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2008
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Abstract

A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, smax, approaching the full dimension of the system, D. We show that almost all subspaces with dimension s = smax are completely entangled and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n = D - smax. This condition holds for almost all sets of states of all multipartite systems and reveals something surprising. The criterion is identical for separable and nonseparable states: entanglement makes no difference.

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Journal of Physics A: Mathematical and Theoretical

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41

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© 2008 Institute of Physics Publishing. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.Please refer to the journal's website for access to the definitive, published version.

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Quantum Information, Computation and Communication

Mathematical Sciences

Physical Sciences

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