Almost every set of $N\ge d+1$ orthogonal states on $d^{\otimes n}$ is locally indistinguishable

Abstract

I consider the problem of deterministically distinguishing the state of a multipartite system, from a set of $N\ge d+1$ orthogonal states, where $d$ is the dimension of each party's subsystem. It is shown that if the set of orthogonal states is chosen at random, then there is a vanishing probability that this set will be perfectly distinguishable under the restriction that the parties use only local operations on their subsystems and classical communication amongst themselves.

5 pages, no figures, comments welcome

References in corpus (4)

• Multipartite Nonlocality without Entanglement in Many Dimensions
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Local distinguishability with preservation of entanglement
• Local Distinguishability of Orthogonal Quantum States and Generators of SU(N)

Cited by in corpus (4)

• Local hypothesis testing between a pure bipartite state and the white noise state
• Framework for distinguishability of orthogonal bipartite states by one-way local operations and classical communication
• Devising local protocols for multipartite quantum measurements
• Exploration of nonlocalities in ensembles consisting of bipartite quantum states