Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions

TL;DR

This paper explores the link between quantum maximum entropy inference discontinuities and quantum phase transitions, proposing quantum conditional mutual information as a new indicator for detecting non-local transitions in the thermodynamic limit.

Contribution

It reveals the connection between entropy inference discontinuities and non-local quantum phase transitions, introducing quantum conditional mutual information as a detection tool.

Findings

Discontinuity in maximum entropy inference indicates non-local quantum phase transitions.

Local density matrices change smoothly at the transition point.

Quantum conditional mutual information effectively detects non-local transitions.

Abstract

In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit.