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Ordering states with coherence measures
Quantum Physics · Submitted 15 Jan 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The quantification of quantum coherence has attracted a growing attention, and based on various physical contexts, several coherence measures have been put forward. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | An interesting question is whether these coherence measures give the same ordering when they are used to quantify the coherence of quantum states. | gap 0.61 | 0.05 | 0.04 | unclear 0.62 |
| s2 | 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. | result 0.55 | 0.92 | 0.82 | asserted 1.00 |
| s3 | 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. | result 0.71 | 0.93 | 0.24 | asserted 0.99 |
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The paper
Original 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.
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How the literature uses it
3 arXiv papers cite this in 7 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
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By a diagonal and unitary matrix [ref] , $ρ(x,y,z)$ can be transformed into a state with the form
Ordering states of Tsallis relative $\alpha$-entropies of coherence · ordering states with $C_α$ and $C_l_1$ for single-qubit mixed states · 0.87
Cites it as background 2 papers
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Many further discussions about quantum coherence were aroused [ref] .
Ordering states of Tsallis relative $\alpha$-entropies of coherence · Introduction · 1.00
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The importance of coherence encourages a lot of further studies on this subject [ref] .
Dynamics of cohering and decohering power under Markovian channels · Introduction · 0.82
What it cites · 3 sentences without a confident label
Cites as background 2 papers
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The general criterion has triggered the community's great interest [ref] ,and based on the criterion, various concrete measures of coherence have been given.
Operational Resource Theory of Coherence · Introduction · 0.85
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It has many significant applications in various subjects, such as quantum optics [ref] , quantum information [ref] , quantum biology [ref] , and thermodynamics [ref] .
Thermodynamics of quantum coherence · Introduction · 0.86
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