Detecting the local indistinguishability of maximally entangled states

Abstract

By incorporating the asymmetry of local protocols, i.e., some party has to start with a nontrivial measurement, into an operational method of detecting the local indistinguishability proposed by Horodecki {\it et al.} [Phys.Rev.Lett. 90 047902 (2003)], we derive a computable criterion to efficiently detect the local indistinguishability of maximally entangled states. Locally indistinguishable sets of $d$ maximally entangled states in a $d\otimes d$ system are systematically constructed for all $d\ge 4$ as an application. Furthermore, by exploiting the fact that local protocols are necessarily separable, we explicitly construct small sets of $k$ locally indistinguishable maximally entangled states with the ratio $k/d$ approaching 3/4. In particular, in a $d\otimes d$ system with even $d\ge 6$, there always exist $d-1$ maximally entangled states that are locally indistinguishable by separable measurements.

6 pages, 1 table

References in corpus (4)

• Multipartite Nonlocality without Entanglement in Many Dimensions
• Optimal entanglement criterion for mixed quantum states
• Local distinguishability with preservation of entanglement
• Local Distinguishability of Orthogonal Quantum States and Generators of SU(N)

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• Local discrimination of generalized Bell states via commutativity
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• Nonlocal sets of orthogonal multipartite product states with less members