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
We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent c...We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition.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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.1140103261473325+9 种基金115011531110522611275131and 11401106)the Fundamental Research Funds for the Central UniversitiesChina(Grant Nos.15CX08011A and 24720122013)the Natural Science Foundation of Hainan ProvinceChina(Grant Nos.20151005 and 20151010)the Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry
文摘We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition.
