Basis-independent quantum coherence and its distribution

• Published in: Annals of physics Vol. 409; p. 167906
• Main Authors: Radhakrishnan, Chandrashekar, Ding, Zhe, Shi, Fazhan, Du, Jiangfeng, Byrnes, Tim
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01-10-2019
• Subjects: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; DISTRIBUTION; Distribution of coherence; HILBERT SPACE; INFORMATION THEORY; MIXED STATES; Quantum coherence; QUANTUM DECOHERENCE; QUANTUM INFORMATION; Quantum information theory; QUANTUM SYSTEMS; TRANSFORMATIONS; Distribution of coherence; Quantum coherence; Quantum information theory
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2019.04.020

We analyze a basis-independent definition of quantum coherence. The maximally mixed state is used as the reference state, which allows for a way of defining coherence that is invariant under arbitrary unitary transformations. Such a basis independent formulation is related to the purity of system rather than the superposition in a particular basis. The basis-independent approach is applied to finding the distribution of the coherence within a multipartite system, where the contributions due to correlations between the subsystems and within each subsystem are isolated. The use of the square root of the Jensen–Shannon divergence allows for inequality relations to be derived between these quantities, giving a geometrical picture within the Hilbert space of the system. We describe the relationship between the basis-independent and the basis-dependent approaches, and argue that many advantages exist for the former method. The formalism is illustrated with several numerical examples which show that the states can be characterized in a simple and effective manner.