Logarithmic coherence measure related to function f based on the standard convex roof construction

Abstract

In this paper, we introduce a logarithmic coherence measure that is associated with function f, based on the standard convex roof construction. We define the logarithmic coherence for pure states using the logarithmic function and extend this definition to mixed states, terming it the logarithmic coherence measure related to function f. We show that the logarithmic coherence measure related to function f is a proper coherence measure, fulfilling the four conditions that a coherence measure should satisfy. Moreover, we also investigate some interesting properties of the logarithmic coherence measure related to function f, including the subadditivity, superadditivity and the existence of its regularized version. We find that the logarithmic coherence measure related to function f can be either subadditive or superadditive, depending on certain conditions. Finally, we discuss the relationships among different logarithmic coherence measures, as well as their connections with other coherence measures.