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

• Published in: Annals of physics Vol. 431; p. 168550
• Main Authors: Halder, Saronath, Sen, Ujjwal
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.08.2021
• Subjects: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Inequivalent class; Local operation; MIXED STATE; MIXED STATES; PURE STATES; QUANTUM ENTANGLEMENT; QUANTUM SYSTEMS; QUBITS; Separable measurement; Uncompletable entangled basis; Unextendible entangled basis; Separable measurement; Inequivalent class; Uncompletable entangled basis; Unextendible entangled basis; Local operation
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2021.168550

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. •Local indistinguishability of orthogonal quantum states.•Bipartite and multipartite quantum ensembles.•Unextendible entangled bases and uncompletable entangled bases.•Two-element locally indistinguishable quantum ensembles.•Multiparty unextendible entangled bases with unextendibility in all partitions.