1. Quantum Incoherence Based Simultaneously on k Bases.
- Author
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Wang, Pu, Guo, Zhihua, and Cao, Huaixin
- Subjects
- *
COHERENT states , *QUANTUM coherence , *STATISTICAL correlation , *QUANTUM states , *ORTHONORMAL basis - Abstract
Quantum coherence is known as an important resource in many quantum information tasks, which is a basis-dependent property of quantum states. In this paper, we discuss quantum incoherence based simultaneously on k bases using Matrix Theory Method. First, by defining a correlation function m (e , f) of two orthonormal bases e and f, we investigate the relationships between sets I (e) and I (f) of incoherent states with respect to e and f. We prove that I (e) = I (f) if and only if the rank-one projective measurements generated by e and f are identical. We give a necessary and sufficient condition for the intersection I (e) ⋂ I (f) to include a state except the maximally mixed state. Especially, if two bases e and f are mutually unbiased, then the intersection has only the maximally mixed state. Secondly, we introduce the concepts of strong incoherence and weak coherence of a quantum state with respect to a set B of k bases and propose a measure for the weak coherence. In the two-qubit system, we prove that there exists a maximally coherent state with respect to B when k = 2 and it is not the case for k = 3 . [ABSTRACT FROM AUTHOR]
- Published
- 2022
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