The quantification of the quantumness of a quantum ensemble has theoretical and practical signif- icance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles usi...The quantification of the quantumness of a quantum ensemble has theoretical and practical signif- icance 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 con- stituent 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.展开更多
基金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.
文摘The quantification of the quantumness of a quantum ensemble has theoretical and practical signif- icance 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 con- stituent 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.
