Ordering states with coherence measures

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 quan...

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Bibliographic Details
Published in:Quantum information processing 2016-10, Vol.15 (10), p.4189-4201
Main Authors: Liu, C. L., Yu, Xiao-Dong, Xu, G. F., Tong, D. M.
Format: Article
Language:English
Subjects:
Coherence
Data Structures and Information Theory
Entropy
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum phenomena
Quantum Physics
Spintronics
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Summary: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.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-016-1398-5