Abstract
We define and analyze measures of correlations for bipartite states based on trace distance. For Bell diagonal states of two qubits, in addition to the known expression for quantum correlations using this metric, we provide analytic expressions for the classical and total correlations. The ensuing hierarchy of correlations based on trace distance is compared to those based on relative entropy and Hilbert–Schmidt norm. Although some common features can be found, the trace distance measure is shown to differentiate from the others in that the closest uncorrelated state to a given bipartite quantum state is not given by the product of the marginals, and further, the total correlations are strictly smaller than the sum of the quantum and classical correlations. We compare the various correlation measures in two dynamical non-Markovian models, locally applied phase-flip channels and random external fields. It is shown that the freezing behavior, observed across all known valid measures of quantum correlations for Bell diagonal states under local phase-flip channels, occurs for a larger set of starting states for the trace distance than for the other metrics.
Highlights
We define and analyze measures of correlations for bipartite states based on trace distance
We construct a unified hierarchy of quantum, classical and total correlations in bipartite quantum states based on the trace distance
For Bell diagonal states of two qubits, we complement the study of Nakano et al [18] and Paula et al [19] by deriving closed expressions for the classical and total correlations defined via trace distance
Summary
We consider the class of two-qubit Bell diagonal states (or states with maximally mixed marginals [27]) expressed in the Bloch representation as ρB. The trace distance discord quantifying quantum correlations of an arbitrary state ρAB ≡ ρ of a bipartite system AB, as revealed on subsystem A, can be defined as [18, 19]. In [18], it has been proven that when A is a qubit, the trace distance discord is equivalent to the so-called negativity of quantumness, which quantifies the minimum negativity of entanglement [2] created with an apparatus during a local projective measurement of subsystem. A closed expression for the trace distance discord DTD(ρB) for arbitrary Bell diagonal states ρB of two qubits was obtained in [18, 19]. For completeness, we construct the explicit form of the closest classical state χρB to an arbitrary Bell diagonal state ρB, which attains the minimum in equation (6) resulting in the expression given by equation (9) for the trace distance discord
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
