Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions

TL;DR

This paper introduces new quantum correlation measures based on sandwiched relative entropies, demonstrating their effectiveness as order parameters in quantum phase transitions, especially in the transverse quantum Ising model, outperforming traditional measures.

Contribution

The authors propose novel quantum correlation measures using sandwiched relative Rényi and Tsallis entropies, showing improved detection of quantum critical points and finite-size scaling over existing measures.

Findings

Measures detect quantum critical points accurately.

They outperform traditional quantum discord in finite-size scaling.

They remove unquieting features of nearest-neighbor quantum discord.

Abstract

Quantum discord is a measure of quantum correlations beyond the entanglement-separability paradigm. It is conceptualized by using the von Neumann entropy as a measure of disorder. We introduce a class of quantum correlation measures as differences between total and classical correlations, in a shared quantum state, in terms of the sandwiched relative R\'{e}nyi and Tsallis entropies. We compare our results with those obtained by using the traditional relative entropies. We find that the measures satisfy all the plausible axioms for quantum correlations. We evaluate the measures for shared pure as well as paradigmatic classes of mixed states. We show that the measures can faithfully detect the quantum critical point in the transverse quantum Ising model and find that they can be used to remove an unquieting feature of nearest-neighbor quantum discord in this respect. Furthermore, the measures provide better finite-size scaling exponents of the quantum critical point than the ones for other known order parameters, including entanglement and information-theoretic measures of quantum correlations.