Fluctuation-Dissipation Theorem and Information Geometry in Open Quantum Systems

TL;DR

This paper establishes a fluctuation-dissipation theorem for open quantum systems using information geometry, introducing fidelity susceptibility and correlators to analyze phase transitions and proposing a polynomial proxy for experimental detection.

Contribution

It introduces a novel fluctuation-dissipation relation based on information-theoretic measures and develops a geometric framework for analyzing quantum phase transitions.

Findings

Fidelity susceptibility scales differently across phases.

The quantum information metric is generally non-analytic.

A polynomial proxy for phase transition detection is proposed.

Abstract

We propose a fluctuation-dissipation theorem in open quantum systems from an information-theoretic perspective. We define the fidelity susceptibility that measures the sensitivity of the systems under perturbation and relate it to the fidelity correlator that characterizes the correlation behaviors for mixed quantum states. In particular, we determine the scaling behavior of the fidelity susceptibility in the strong-to-weak spontaneous symmetry breaking (SW-SSB) phase, strongly symmetric short-range correlated phase, and the quantum critical point between them. We then provide a geometric perspective of our construction using distance measures of density matrices. We find that the metric of the quantum information geometry generated by perturbative distance between density matrices before and after perturbation is generally non-analytic. Finally, we design a polynomial proxy that can in principle be used as an experimental probe for detecting the SW-SSB and phase transition through quantum metrology. In particular, we show that each term of the polynomial proxy is related to the R\'enyi versions of the fidelity correlators.