Note on quantum discord

TL;DR

This paper introduces new criteria for detecting quantum discord in two-qubit and qubit-qudit systems, providing analytical bounds and demonstrating effectiveness through examples, advancing understanding of quantum correlations beyond entanglement.

Contribution

It proposes a zero-discord detection criterion based on partial transposition and extends it to qubit-qudit systems, along with analytical bounds for geometric quantum discord and work deficit.

Findings

Effective discord detection criteria demonstrated with examples

Analytical lower bounds for geometric quantum discord established

Lower bounds for work deficit derived from GQD bounds

Abstract

Quantum discord goes beyond entanglement and exists in a wide range of quantum states that may be separable, playing a crucial role in quantum information tasks. In this paper, we firstly proposed a zero-discord criterion for two-qubit system based on the partial transposition of density matrix, and then extended it to the qubit-qudit system. By detailed examples we demonstrate the effectiveness of these criteria in detecting discord. Moreover, we provide an analytical lower bound of geometric quantum discord(GQD) using eigenvalue vectors of density matrix. Finally, we presented a one-way work deficit lower bound based on our lower bound of GQD.