Maximally discordant mixed states of two qubits

TL;DR

This paper investigates the relationship between classical and quantum correlations in two-qubit states, identifying states with maximal discord, and analyzing how these correlations manifest across different state ranks.

Contribution

It introduces the family of states that maximize discord for given classical correlations and compares discord with entanglement in mixed states.

Findings

Largest discord for mixed states exceeds that of pure states.

States with maximal discord can be separable, not necessarily entangled.

Quantum and classical correlations vary with state rank and are statistically characterized.

Abstract

We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separable. Finally, by random generation of density matrices uniformly distributed over the whole Hilbert space, we quantify the frequency of the appearance of quantum and classical correlations for different ranks.