Epsilon-smooth measure of coherence

Abstract

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.

arXiv commentPublished version

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Cited by in corpus (8)

• Efficient estimation of multipartite quantum coherence
• Certifying quantum memories with coherence
• Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
• Continuity of robustness measures in quantum resource theories
• Witnessing quantum coherence with prior knowledge of observables
• No-go theorems for deterministic purification and probabilistic enhancement of coherence
• The tightness of multipartite coherence from spectrum estimation
• Distance-based measures and Epsilon-measures for measurement-based quantum resources