Information dynamics in decohered quantum memory with repeated syndrome measurements: a dual approach

TL;DR

This paper investigates the information dynamics in decohered quantum memories under repeated syndrome measurements, using a dual statistical mechanics approach to analyze phase transitions in information encoding.

Contribution

It introduces a dual statistical mechanics model for quantum memory information dynamics, linking phase transitions to decoding performance in stabilizer codes.

Findings

Identifies a thermal phase transition corresponding to decoding thresholds.

Develops a unified framework for analyzing information flow in quantum error correction.

Applies the model to surface, repetition, and XZZX codes, revealing their phase transition behaviors.

Abstract

Measurements can detect errors in a decohered quantum memory allowing active error correction to increase the memory time. Previous understanding of this mechanism has focused on evaluating the performance of error correction algorithms based on measurement results. In this work, we instead intrinsically characterize the information dynamics in a quantum memory under repeated measurements, using coherent information and relative entropy. We consider the dynamics of a $d$-dimensional stabilizer code subject to Pauli errors and noisy stabilizer measurements and develop a $(d+1)$-dimensional statistical mechanics model for the information-theoretic diagnostics. Our model is dual to the model previously obtained for the optimal decoding algorithm, and the potential decoding transition in the quantum memory again manifests as a thermal phase transition in the statistical mechanics model. We explicitly derive the model and study the phase transition in information encoding in three examples: surface codes, repetition codes, and the XZZX code.