Frontiers of Physics

, 13:130309 | Cite as

Quantifying the quantumness of ensembles via unitary similarity invariant norms

  • Xian-Fei Qi
  • Ting Gao
  • Feng-Li Yan
Research article


The quantification of the quantumness of a quantum ensemble has theoretical and practical significance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles using the unitary similarity invariant norms of the commutators of the constituent density operators of an ensemble. Rigorous proof shows that they share desirable properties for a measure of quantumness, such as positivity, unitary invariance, concavity under probabilistic union, convexity under state decomposition, decreasing under coarse graining, and increasing under fine graining. Several specific examples illustrate the applications of these measures of quantumness in studying quantum information.


the quantumness of quantum ensemble measures of quantumness of quantum ensembles unitary similarity invariant norms 

PACS numbers

03.67.Mn 03.65.Ud 03.67.-a 



This work was supported by the National Natural Science Foundation of China under Grant Nos. 11371005 and 11475054 and the Hebei Natural Science Foundation under Grant Nos. A2016205145 and A2018205125.


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangChina
  2. 2.College of Physics Science and Information EngineeringHebei Normal UniversityShijiazhuangChina

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