Non-commutativity and Local Indistinguishability of Quantum States

Abstract

We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a complete set of pure orthogonal product states. A constructive distinguishing procedure to obtain the concrete local measurements and classical communications is given. The non-commutativity of ensembles can be also used to characterize the quantumness for classical-quantum or quantum-classical correlated states.

arXiv comment12 pages

References in corpus (13)

• Introducing Quantum Discord
• The classical-quantum boundary for correlations: discord and related measures
• Quantum Nonlocality without Entanglement
• On the Power of One Bit of Quantum Information
• Unextendible Product Bases and Bound Entanglement
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Nonlocality, Asymmetry, and Distinguishing Bipartite States
• Distinguishability of the Bell states
• Quantum discord and local demons
• A framework for bounding nonlocality of state discrimination
• Quantum state filtering and discrimination between sets of Boolean functions
• Distinguishing a set of full product bases needs only projective measurements and classical communication
• Asymptotically perfect discrimination in the LOCC paradigm

Cited by in corpus (5)

• Quantum coherence and geometric quantum discord
• Nonlocality of orthogonal product basis quantum states
• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
• Constructing locally indistinguishable orthogonal product bases in an $m\otimes n$ system
• Brief Theory of Multiqubit Measurement