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We plot the geometry of several distance-based quantifiers of coherence for Bell-diagonal states. We find that along with both $l_{1}$ norm and relative entropy of coherence changes continuously from zero to one, their surfaces move from the separable regions to the entangled regions. Based on this fact, it is more illuminating to use an intuitive geometry to explain quantum states with nonzero coherence can be used for entanglement creation, rather than the other way around. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equal to its relative entropy of coherence and depict the surfaces of 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 coherence under local nondissipative channels decrease.
The one-way quantum deficit, a measure of quantum correlation, can exhibit for X quantum states the regions (subdomains) with the phases $Delta_0$ and $Delta_{pi/2}$ which are characterized by constant (i.e., universal) optimal measurement angles, co
We investigate the geometric picture of the level surfaces of quantum entanglement and geometric measure of quantum discord (GMQD) of a class of X-states, respectively. This pictorial approach provides us a direct understanding of the structure of en
Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. In this paper, we discuss thoroughly the case of two-qubit rank-two stat
Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. Exact results are known only for very special states, namely, two-qubit
We present an efficient method to solve the quantum discord of two-qubit X states exactly. A geometric picture is used to clarify whether and when the general POVM measurement is superior to von Neumann measurement. We show that either the von Neuman