Generic local distinguishability and completely entangled subspaces
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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.
Journal of Physics A: Mathematical and Theoretical
Copyright 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.
Quantum Information, Computation and Communication