Quantum Discord and Logarithmic Negativity in the Generalized n-qubit Werner State

TL;DR

This paper investigates quantum correlations in generalized n-qubit Werner states, revealing that quantum discord saturates linearly in the thermodynamic limit while entanglement increases non-uniformly and saturates, supported by analytical and numerical evidence.

Contribution

It extends the analysis of quantum discord and entanglement to higher-dimensional Werner states, providing new insights into their asymptotic behaviors.

Findings

Quantum discord saturates to a line with unit slope in the thermodynamic limit.

Entanglement increases non-uniformly with the number of qubits and saturates.

Results are supported by both analytical calculations and numerical simulations.

Abstract

Quantum Discord (QD) is a measure of the total quantum non-local correlations of a quantum system. The formalism of quantum discord has been applied to various two-qubit mixed states and it has been reported that there is a non-zero quantum discord even when the states are unentangled. To this end, we have calculated the Quantum Discord for higher than two qubit mixed state, that is, the generalized n-qubit Werner state with a bipartite split. We found that the QD saturates to a straight line with unit slope in the thermodynamic limit. Qualitative studies of entanglement between the two subsystems using logarithmic negativity revealed that the entanglement content between them increases non-uniformly with the number of qubits leading to its saturation. We have proved the above claims both analytically and numerically.