Quantifying the coherence of pure quantum states

Abstract

In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence. We then use this result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states. We define the trace distance of entanglement and show that it coincides with the trace distance of coherence for pure states. Finally, we give an alternate proof to a recent result that the ${\ell }_1$ measure of coherence of a pure state is never smaller than its relative entropy of coherence.

11 pages, trace distance of entanglement is new in v2

References in corpus (8)

• Measuring Quantum Coherence with Entanglement
• Robustness of coherence: An operational and observable measure of quantum coherence
• A complete family of separability criteria
• Trace-distance measure of coherence
• Quantifying Entanglement with Witness Operators
• Quantifying Superposition
• Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
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Cited by in corpus (19)

• Quantum Coherence as a Resource
• Operational one-to-one mapping between coherence and entanglement measures
• Genuine quantum coherence
• Convex geometry of quantum resource quantification
• Quantifying the resource content of quantum channels: An operational approach
• Logarithmic coherence: Operational interpretation of ${\ell }_1$-norm coherence
• Discordlike correlation of bipartite coherence
• Activation of entanglement from quantum coherence and superposition
• Some notes on the robustness of k-coherence and k-entanglement
• Trace distance measure of coherence for a class of qudit states
• Coherence measures induced by norm functions
• The modified trace distance of coherence is constant on most pure states
• Probabilistic state synthesis based on optimal convex approximation
• Twirling channels have minimal mixed-unitary rank
• Experimental quantification of quantum coherence for a set of quantum states
• Dynamics of cohering and decohering power under Markovian channels
• Completely positive completely positive maps (and a resource theory for non-negativity of quantum amplitudes)
• Frame-dependent coherence of a quantum state
• Polaron effects on the information backflow in Jaynes-Cummings model