Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise

TL;DR

This paper introduces a method to stabilize symmetry-protected topological order in open quantum systems with heralded noise, using local correction protocols that confine errors and maintain order under certain noise conditions.

Contribution

It develops a local correction protocol leveraging heralded noise to preserve SPT order in open quantum systems, supported by numerical and analytical analysis.

Findings

The protocol stabilizes SPT order against low rates of heralded decoherence.

SPT order is lost via a directed percolation transition at higher noise rates.

Local SPT order persists with a diverging correlation length as heralded error fraction decreases.

Abstract

We present a family of local quantum channels whose steady-states exhibit stable mixed-state symmetry-protected topological (SPT) order. Motivated by recent experimental progress on "erasure conversion" techniques that allow one to identify ($\textit{herald}$) decoherence processes, we consider open systems with biased erasure noise, which leads to strongly symmetric heralded errors. We utilize this heralding to construct a local correction protocol that effectively confines errors into short-ranged pairs in the steady-state. Using a combination of numerical simulations and mean-field analysis, we show that our protocol stabilizes SPT order against a sufficiently low rate of decoherence. As the rate of heralded noise increases, SPT order is eventually lost through a directed percolation transition. We further find that while introducing unheralded errors destroys SPT order in the limit of long length- and time-scales, the correction protocol is sufficient for ensuring that local SPT order persists, with a correlation length that diverges as $\xi \sim (1-f_e)^{-1/2}$, where $f_e$ is the fraction of errors that are heralded.