Orthogonality And Distinguishability: Criterion For Local Distinguishability of Arbitrary Orthogonal States

Abstract

We consider deeply the relation between the orthogonality and the distinguishability of a set of arbitrary states (including multi-partite states). It is shown that if a set of arbitrary states can be distinguished by local operations and classical communication (LOCC), \QTR{it}{\}each of the states can be written as a linear combination of product vectors such that all product vectors of one of the states are orthogonal to the other states. With this result we then prove a simple necessary condition for LOCC distinguishability of a class of orthogonal states. These conclusions may be useful in discussing the distinguishability of orthogonal quantum states further, understanding the essence of nonlocality and discussing the distillation of entanglement.

Revision to appear PRA

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Cited by in corpus (28)

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• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• Bipartite subspaces having no LOCC-distinguishable bases
• A framework for bounding nonlocality of state discrimination
• Distinguishability of Quantum States by Separable Operations
• Local distinguishability with preservation of entanglement
• LOCC distinguishability of unilaterally transformable quantum states
• Limitations on separable measurements by convex optimization
• More nonlocality with less purity
• Distinguishing a set of full product bases needs only projective measurements and classical communication
• Multiparty data hiding of quantum information
• Constructing locally indistinguishable orthogonal product bases in an $m\otimes n$ system
• Entanglement Cost of Nonlocal Measurements
• Asymptotically perfect discrimination in the LOCC paradigm
• Detecting the local indistinguishability of maximally entangled states
• Difficulty of distinguishing product states locally
• Local Distinguishability of Orthogonal Quantum States and Generators of SU(N)
• Discrimination of two-qubit unitaries via local operations and classical communication
• Building one-time memories from isolated qubits
• Separability and entanglement in superpositions of quantum states
• Unextendible entangled bases and more nonlocality with less entanglement
• Incompatibility of local measurements provide advantage in local quantum state discrimination
• Local distinguishability of quantum states in multipartite System
• Locality of Orthogonal Product States via Multiplied Copies
• The construction of sets with strong quantum nonlocality using fewer states
• Exploration of nonlocalities in ensembles consisting of bipartite quantum states
• The Independence of Distinguishability and the Dimension of the System