Geometry of Quantum Coherence for Two Qubit X States

Yao-Kun Wang, Lian-He Shao, Shao-Ming Fei, and Zhi-Xi Wang

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Submission date: 21. Aug. 2019
Pages: 12
published in: International journal of theoretical physics, 58 (2019) 7, p. 2372-2383 
DOI number (of the published article): 10.1007/s10773-019-04129-0
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Abstract:
We investigate the geometry with respect to several distance-based quantifiers of coherence for Bell-diagonal states. We find that as both l₁ norm and relative entropy of coherence vary continuously from zero to one, their related geometric surfaces move from the region of separable states to the region of entangled states, a fact illustrating intuitively that quantum states with nonzero coherence can be used for entanglement creation. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equals to its relative entropy of coherence, and depict the surfaces related to the equality. We give surfaces of relative entropy of coherence for X states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherences under local nondissipative channels decrease.