Generic local distinguishability and completely entangled subspaces

TL;DR

This paper investigates the properties of completely entangled subspaces in multipartite quantum systems, revealing that most small subspaces are completely entangled and establishing a surprising criterion for local distinguishability of quantum states.

Contribution

It proves that almost all subspaces below a certain size are completely entangled and derives a universal criterion for local distinguishability of quantum states regardless of entanglement.

Findings

Most subspaces with dimension ≤ S are completely entangled.

n random pure states are unambiguously locally distinguishable if n ≤ D - S.

The distinguishability criterion is the same for separable and entangled states.

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, 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.