A quantum measure of coherence and incompatibility

Abstract

The well-known two-slit interference is understood as a special relation between observable (localization at the slits) and state (being on both slits). Relation between an observable and a quantum state is investigated in the general case. It is assumed that the amount of ceherence equals that of incompatibility between observable and state. On ground of this, an argument is peresented that leads to a natural quantum measure of coherence, called "coherence or incompatibility information". Its properties are studied in detail making use of 'the mixing property of relative entropy' derived in this article. A precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intutitive point of view. Convexity of the measure is proved, and thus the fact that it is an information entity is established. A few more detailed properties of coherence information are derived with a view to investigate final-state entanglement in general repeatable measurement, and, more importantly, general bipartite entanglement in follow ups of this study.

19 GS pages; supercedes quant-ph/0309211

References in corpus (5)

• Classical Correlations and Entanglement in Quantum Measurements
• On Mutual Information in Multipartite Quantum States and Equality in Strong Subadditivity of Entropy
• Chains of Quasi-Classical Informations for Bipartite Correlations and the Role of Twin Observables
• The role of coherence entropy of physical twin observables in entanglement
• On the meaning of entanglement in quantum measurement

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• Interpreting quantum coherence through a quantum measurement process
• Quantum coherence fluctuation relations
• A Review of Unitary Quantum Premeasurement Theory An Algebraic Study of Basic Kinds of Premeasurements
• Critical Assessment of Wave-Particle Complementarity via Derivation from Quantum Mechanics
• Distance-based approach to quantum coherence and nonclassicality
• Phase-sensitive superposition of quantum states