Generic local distinguishability and completely entangled subspaces

Details Generic local distinguishability and completely entangled subspaces Generic local distinguishability and completely entangled subspaces

2007-09-26

arxiv.org/abs/0709.4238v2

J. Phys. A 41, 375305 (2008)

Physics

Quantum Physics

12 pages

Scientific paper

10.1088/1751-8113/41/37/375305

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, S, approaching the full dimension of the system, D. We show that almost all subspaces with dimension less than or equal to S 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 does not exceed D-S. This condition holds for almost all sets of states of all multipartite systems, and reveals something surprising. The criterion is identical for separable and for nonseparable states: entanglement makes no difference.

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