Local distinguishability of orthogonal 2\otimes3 pure states

Abstract

We present a complete characterization for the local distinguishability of orthogonal $2\otimes 3$ pure states except for some special cases of three states. Interestingly, we find there is a large class of four or three states that are indistinguishable by local projective measurements and classical communication (LPCC) can be perfectly distinguishable by LOCC. That indicates the ability of LOCC for discriminating $2\otimes 3$ states is strictly more powerful than that of LPCC, which is strikingly different from the case of multi-qubit states. We also show that classical communication plays a crucial role for local distinguishability by constructing a class of $m\otimes n$ states which require at least $2\min \{m,n\}-2$ rounds of classical communication in order to achieve a perfect local discrimination.

10 pages (revtex4), no figures. This is only a draft. It will be replaced with a revised version soon. Comments are welcome

References in corpus (4)

• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Local distinguishability with preservation of entanglement
• Optimal conclusive discrimination of two states can be achieved locally

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