Quantifying coherence in terms of the pure-state coherence

Abstract

Quantifying quantum coherence is a key task in the resource theory of coherence. Here we establish a good coherence monotone in terms of a state conversion process, which automatically endows the coherence monotone with an operational meaning. We show that any state can be produced from some input pure states via the corresponding incoherent channels. It is especially found that the coherence of a given state can be well characterized by the least coherence of the input pure states, so a coherence monotone is established by only effectively quantifying the input pure states. In particular, we show that our proposed coherence monotone is the supremum of all the coherence monotones that give the same coherence for any given pure state. Considering the convexity, we prove that our proposed coherence measure is a subset of the coherence measure based on the convex roof construction. As an application, we give a concrete expression of our coherence measure by employing the geometric coherence of a pure state. We also give a thorough analysis on the states of qubit and finally obtain series of analytic coherence measures.

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• Quantum Discord for multiqubit Systems
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• Skew information-based coherence generating power of quantum channels
• Generalized coherence vector applied to coherence transformations and quantifiers
• An Extention of Entanglement Measures for Pure States
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• No-go theorems for deterministic purification and probabilistic enhancement of coherence
• Quantifying entanglement in terms of an operational way
• Methods of constructing superposition measures
• Behavior of quantum coherence in the ultrastrong and deep strong coupling regimes of light-matter system