Majorization relation in quantum critical systems

TL;DR

This paper explores how local state conversions in quantum critical systems change at phase transitions, revealing a connection between majorization relations and quantum phase transition properties.

Contribution

It introduces a novel method using majorization relations to analyze LOCC convertibility in quantum critical systems, especially at phase transitions.

Findings

LOCC convertibility changes near the phase transition point

Majorization relation reveals differences in ground state convertibility

Comparison with Renyi entropy enhances understanding of quantum phase transitions

Abstract

The most basic local conversion is local operations and classical communications (LOCC), which is also the most natural restriction in quantum information processing. We investigate the conversions between the ground states in quantum critical systems via LOCC and propose an novel method to reveal the different convertibility via majorization relation when a quantum phase transition occurs. The ground-state local convertibility in the one-dimensional transverse field Ising model is studied. It is shown that the LOCC convertibility changes nearly at the phase transition point. The relation between the order of quantum phase transitions and the LOCC convertibility is discussed. Our results are compared with the corresponding results using the Renyi entropy and the LOCC convertibility with assisted entanglement.