Problem of quantifying quantum correlations with non-commutative discord

In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure...

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Detalles Bibliográficos
Autores: Majtey, Ana Paula, Bussandri, Diego G., Osán, Tristán Martín, Lamberti, Pedro Walter, Valdés-Hernández, A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/63765
Acceso en línea:http://hdl.handle.net/11336/63765
Access Level:acceso abierto
Palabra clave:Bipartite Systems
Hilbert&Ndash;Schmidt Norm
Non-Commutative Discord
Quantum Correlations
Quantum Correlations Measure
Quantum Discord
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
Descripción
Sumario:In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt’s is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt’s. In addition, the resulting measure inherits the main properties of Guo’s measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo’s measure can result in an overestimation of quantum correlations. However, since Guo’s measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.