We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
69/2019
Geometry of Quantum Coherence for Two Qubit X States
Yao-Kun Wang, Lian-He Shao, Shao-Ming Fei and Zhi-Xi Wang
Abstract
We investigate the geometry with respect to several distance-based quantifiers of coherence for Bell-diagonal states. We find that as both $l_{1}$ 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.
