Unifying approach to the quantification of bipartite correlations by Bures distance

Abstract

The notion of distance defined on the set of states of a composite quantum system can be used to quantify total, quantum and classical correlations in a unifying way. We provide new closed formulae for classical and total correlations of two-qubit Bell-diagonal states by considering the Bures distance. Complementing the known corresponding expressions for entanglement and more general quantum correlations, we thus complete the quantitative hierarchy of Bures correlations for Bell-diagonal states. We then explicitly calculate Bures correlations for two relevant families of states: Werner states and rank-2 Bell-diagonal states, highlighting the subadditivity which holds for total correlations with respect to the sum of classical and quantum ones when using Bures distance. Finally, we analyse a dynamical model of two independent qubits locally exposed to non-dissipative decoherence channels, where both quantum and classical correlations measured by Bures distance exhibit freezing phenomena, in analogy with other known quantifiers of correlations.

18 pages, 4 figures; published version

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• Universal freezing of quantum correlations within the geometric approach
• The dynamics of local quantum uncertainty and trace distance discord for two-qubit X states under decoherence: a comparative study
• Universal evolution of non-classical correlations due to collective spontaneous emission
• Overcoming ambiguities in classical and quantum correlation measures
• Influence of the external pressure on the quantum correlations of molecular magnets
• Characterizing nonclassical correlation using affinity
• Hierarchy of correlation quantifiers comparable to negativity
• Unified scheme for correlations using linear relative entropy
• Comparison of Perfect and Quasi Werner States
• A variational quantum algorithm for entanglement quantification