Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles

Abstract

We relate the phenomenon of local indistinguishability of orthogonal states with the properties of unextendibility and uncompletability of entangled bases for bipartite and multipartite quantum systems. We prove that all two-qubit unextendible entangled bases are of size three and they cannot be perfectly distinguished by separable measurements. We identify a method of constructing two-element orthogonal ensembles, based on the concept of unextendible entangled bases, that can potentially lead to information sharing applications. Two-element ensembles form the fundamental unit of ensembles, and yet does not offer locally indistinguishable ensembles for pure state elements. Going over to mixed states does open this possibility, but can be difficult to identify. The method provided using unextendible entangled bases can be used for their systematic generation. In multipartite systems, we find a class of unextendible entangled bases for which the unextendibility property remains conserved across all bipartitions. We also identify nonlocal operations, local implementation of which require entangled resource states from a higher-dimensional quantum system.

title changed; improved version

References in corpus (7)

• Entanglement detection
• Maximally multipartite entangled states
• Distinguishability of Quantum States by Separable Operations
• Generic local distinguishability and completely entangled subspaces
• Optimal conclusive discrimination of two states can be achieved locally
• A Note on Mutually Unbiased Unextendible Maximally Entangled Bases in ${\mathbb{C}}^2⨂{\mathbb{C}}^3$
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Cited by in corpus (4)

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• Unextendible entangled bases and more nonlocality with less entanglement
• Incompatibility of local measurements provide advantage in local quantum state discrimination
• Unconditionally superposition-robust entangled state in all multiparty quantum systems