Nullity of quantum discord of two-qubit X-state systems

TL;DR

This paper establishes conditions for when quantum discord vanishes in two-qubit X-states, showing it can disappear at finite times due to population degeneracies and coherences, with implications for quantum correlations in dynamical systems.

Contribution

It provides a detailed analysis of nullity conditions for quantum discord in two-qubit X-states, including dynamical behavior and specific models like the Tavis-Cummings system.

Findings

Quantum discord can vanish at finite times despite correlations.

Degeneracy of populations and coherences causes discord nullity.

Discord disappearance depends on initial conditions and can be periodic.

Abstract

The conditions are established for nullity of quantum discord for mixed states of a general two-qubit system whose dynamical behaviour is given by an X-state form density matrix. It is found that quantum discord can vanish at a finite time even in the presence of correlations between qubits. The degeneracy of the populations of the combined states of the qubits and the multi-qubit quantum coherences are shown to be responsible for vanishing of the discord. We illustrate our considerations by examining the coherent-state Tavis-Cummings model in which two qubits interact dispersively with the cavity field. The disappearance of the discord is shown to be dependent on the initial atomic conditions that it may occur at a discrete instance or periodically at discrete instances redistributed over whole range of the evolution time. The nullity of the discord is interpreted as resulting from equal preparation of the spin anti-correlated and spin correlated product states in superposition~states.