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
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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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.