Coherence quantifiers from the viewpoint of their decreases in the measurement process

Abstract

Measurements can be considered as a genuine example of processes that crush quantum coherence. In the case of an observable with degeneracy, the formulations of Lüders and von Neumann are known. These pictures postulate the two different states of a system immediately following the act of measurement. Hence, they are associated with divers variants of coherence losses during the measurement. Recent studies have focused on several ways to characterize quantum coherence appropriately. One of the existing types of quantifier is based on quantum $\alpha$-divergences of the Tsallis type. In this paper, we introduce coherence quantifiers associated with the Lüders picture of quantum measurements. The are shown to satisfy the same properties as coherence $\alpha$-quantifiers related to some orthonormal basis. Further, we consider losses of quantum coherence during a generalized measurement. The proposed approach is exemplified with unambiguous state discrimination; extreme properties of the states to be discriminated are clearly shown.

arXiv comment15 pages, three figures. Published as a contribution to Journal of Physics A Special Issue on Quantum Coherence

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• Resource theory of coherence based on positive-operator-valued measures
• Entropic uncertainty relations from equiangular tight frames and their applications
• Quantum coherence as asymmetry from complex weak values
• Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
• Generalized coherence vector applied to coherence transformations and quantifiers
• Quantifying quantum coherence based on the Tsallis relative operator entropy
• Uncertainty and certainty relations for quantum coherence with respect to design-structured POVMs
• Geometric measures of discordlike quantum correlations based on Tsallis relative entropy