Any $2\otimes n$ subspace is locally distinguishable

Abstract

A subspace of a multipartite Hilbert space is called \textit{locally indistinguishable} if any orthogonal basis of this subspace cannot be perfectly distinguished by local operations and classical communication. Previously it was shown that any $m\otimes n$ bipartite system such that $m>2$ and $n>2$ has a locally indistinguishable subspace. However, it has been an open problem since 2005 whether there is a locally indistinguishable bipartite subspace with a qubit subsystem. We settle this problem by showing that any $2\otimes n$ bipartite subspace is locally distinguishable in the sense it contains a basis perfectly distinguishable by LOCC. As an interesting application, we show that any quantum channel with two Kraus operations has optimal environment-assisted classical capacity.

3 pages (Revtex 4).Comments are welcomed

References in corpus (1)

• Distinguishability of Quantum States by Separable Operations

Cited by in corpus (26)

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• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
• Strong quantum nonlocality with entanglement
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• Strongly nonlocal unextendible product bases do exist
• Strong quantum nonlocality in $N$-partite systems
• $d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Saturating the quantum Cramér-Rao bound using LOCC
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• Strong quantum nonlocality with genuine entanglement in an $N$-qutrit system
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• Strong quantum nonlocality from hypercubes
• Local distinguishability of quantum states in multipartite System
• LOCC protocols with bounded width per round optimize convex functions
• When is the Chernoff Exponent for Quantum Operations finite?
• LOCC distinguishable orthogonal product states with least entanglement resource
• Strongest quantum nonlocality in $N$-partite systems
• The construction of sets with strong quantum nonlocality using fewer states
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• The existence of distinguishable bases in three-dimensional subspaces of qutrit-qudit systems under one-way local operations and classical communication
• Novel methods to construct nonlocal sets of orthogonal product states in arbitrary bipartite high-dimensional system