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Geometry of Quantum Coherence for Two Qubit X States |
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| Authors: | Wang Yao-Kun Shao Lian-He Ge Li-Zhu Fei Shao-Ming Wang Zhi-Xi |
| Institution: | 1.College of Mathematics, Tonghua Normal University, Tonghua, Jilin, 134001, China ;2.Research Center for Mathematics, College of Mathematics, Tonghua Normal University, Tonghua, Jilin, 134001, China ;3.State and Local Joint Engineering Research Center for Advanced Networking and Intelligent Information Services, School of Computer Science, Xi’an Polytechnic University, Xi’an, Shaanxi, 710048, China ;4.The Branch Campus of Tonghua Normal University, Tonghua, Jilin, 134001, China ;5.School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China ;6.Max-Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany ; |
| Abstract: | The geometry of the structure of entanglement and discord for Bell-diagonal states is depicted by Lang and Caves (Phys. Rev. Lett. 105, 150501, 2010). In this paper, 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. |
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