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.

arXiv comment6 pages, 1 table

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Cited by in corpus (17)

• Strong Quantum Nonlocality without Entanglement
• Nonlocality of orthogonal product basis quantum states
• Several nonlocal sets of multipartite pure orthogonal product states
• Local indistinguishability of orthogonal product states
• Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination
• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
• Nonlocality without entanglement in general multipartite quantum systems
• The local distinguishability of any three generalized Bell states
• Bounds on the smallest sets of quantum states with special quantum nonlocality
• On small set of one-way LOCC indistinguishability of maximally entangled states
• Genuine hidden nonlocality without entanglement: from the perspective of local discrimination
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Simple criterion for local distinguishability of generalized Bell states in prime dimension
• Local discrimination of generalized Bell states via commutativity
• Finding out all locally indistinguishable sets of generalized Bell states
• Novel methods to construct nonlocal sets of orthogonal product states in arbitrary bipartite high-dimensional system
• Nonlocal sets of orthogonal multipartite product states with less members