Shanshan Yuwen | Searcharxiv

arXiv2018

Coherence measure: Logarithmic coherence number

We introduce a measure of coherence, which is extended from the coherence rank via the standard convex roof construction, we call it the logarithmic coherence number. This approach is parallel to the Schmidt measure in entanglement theory, We study some interesting properties of the logarithmic coherence number, and show that this quantifier can be considered as a proper coherence measure. We also find that the logarithmic coherence number can be calculated exactly for a large class of states. We give the relationship between coherence and entanglement in bipartite system, and our results are generalized to multipartite setting. Finally, we find that the creation of entanglement with bipartite incoherent operations is bounded by the logarithmic coherence number of the initial system during the process.

quant-ph↗

arXiv2018

Epsilon-smooth measure of coherence

In this paper, by minimizing the coherence quantifiers over all states in an $\epsilon$ ball around a given state, we define a generalized smooth quantifier, called the $\epsilon$-smooth measure of coherence. We use it to estimate the difference between the expected state and the actually prepared state and quantify quantum coherence contained in an actually prepared state, and it can been interpreted as the minimal coherence guaranteed to present in an $\epsilon$ ball around given quantum state. We find that the $\epsilon$-smooth measure of any coherence monotone is still a coherence monotone, but it does not satisfy monotonicity on average under incoherent operations. We show the $\epsilon$-smooth measure of coherence is continuous even if the original coherence quantifier is not. We also study the $\epsilon$-smooth measure of distance-based coherence quantifiers, and some interesting properties are given. Moreover, we discuss the dual form of the $\epsilon$-smooth measure of coherence by maximizing over all states in an $\epsilon$ ball around the given state and show that the dual $\epsilon$-smooth measure of coherence provides an upper bound of one-shot coherence distillation.

quant-ph↗