Ordering states with coherence measures

Abstract

The quantification of quantum coherence has attracted a growing attention, and based on various physical contexts, several coherence measures have been put forward. An interesting question is whether these coherence measures give the same ordering when they are used to quantify the coherence of quantum states. In this paper, we consider the two well-known coherence measures, the $l_1$ norm of coherence and the relative entropy of coherence, to show that there are the states for which the two measures give a different ordering. Our analysis can be extended to other coherence measures, and as an illustration of the extension we further consider the formation of coherence to show that the $l_1$ norm of coherence and the formation of coherence, as well as the relative entropy of coherence and the coherence of formation, do not give the same ordering too.

7 pages, 1 figure

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• Measuring Coherence with Entanglement Concurrence
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• Quantum coherence quantifiers based on the Rényi $\alpha$-relative entropy
• Measures of imaginarity and quantum state order
• Superadditivity of convex roof coherence measures
• Dynamics of coherence-induced state ordering under Markovian channels
• Ordering states with various coherence measures
• The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
• Incoherent Gaussian equivalence of $m-$mode Gaussian states
• Frozen condition of quantum coherence
• Parameterized coherence measure
• A note on robustness of coherence for multipartite quantum states
• Dynamics of cohering and decohering power under Markovian channels
• The $n$-th decay rate of coherence for Bell-diagonal states under quantum channels
• Comparing coherence measures for X states: Can quantum states be ordered based on quantum coherence?
• Time evolution of quantum correlations in presence of state dependent bath