The pairwise correlations in a multi-qubit state are quantified through a linear variant of relative entropy. In particular, we derive the explicit expressions of total, quantum and classical bipartite correlations. Two different bi-partioning schemes are considered. We discuss the derivation of closest product, quantum–classical and quantum–classical product states. We also investigate the additivity relation between the various pairwise correlations existing in pure and mixed states. As illustration, some special cases are examined.
In this paper, we introduce and study unified
(r,s)-relative entropy and quantum unified
(r,s)-relative entropy, in particular, our main results of quantum unified
(r,s)-relative entropy are established on the separable complex Hilbert spaces. Moreover, the entanglement-measure of states due to the quantum unified
(r,s)-relative entropy is considered, too. Our results improved a uncorrect statement on the monotone property of entanglement-measure function.
The distance between a quantum state and its closest state not having a certain property has been used to quantify the amount of correlations corresponding to that property. This approach allows a unified view of the various kinds of correlations present in a quantum system. In particular, using relative entropy as a distance measure, total correlations can be meaningfully separated into a quantum part and a classical part thanks to an additive relation involving only the distances between states. Here we investigate a unified view of correlations using as a distance measure the square norm, which has already been used to define the so-called geometric quantum discord. We thus also consider geometric quantifiers for total and classical correlations, finding, for a quite general class of bipartite states, their explicit expressions. We analyze the relationship among geometric total, quantum, and classical correlations, and we find that they no longer satisfy a closed additivity relation.