A Noisy Approach to Intrinsically Mixed-State Topological Order

TL;DR

This paper introduces a framework for understanding mixed-state topological order in 2D systems affected by local correlated errors, revealing new phenomena like quantum memory and chiral order in decohered states.

Contribution

It presents a novel theoretical approach to analyze intrinsically mixed-state topological order, connecting decoherence, anyon gauging, and topological codes in a unified framework.

Findings

Decohered states can encode quantum and classical memory.

Gauging out anyons leads to intrinsically mixed topological order.

Examples include chiral and non-modular topological phases.

Abstract

We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed-state can display intrinsically mixed-state topological order (imTO) -- topological order which is not expected to occur in the ground state of 2D local gapped Hamiltonians. Specifically, we show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, is more naturally phrased as, and provides a physical mechanism for, ``gauging out" anyons in the original Hilbert space. We find that gauging out anyons generically results in imTO, with the decohered mixed-state strongly symmetric under certain anomalous 1-form symmetries. This framework lays bare a striking connection between the decohered density matrix and topological subsystem codes, which can appear as anomalous surface states of 3D topological orders. Through a series of examples, we show that the decohered state can display a classical memory, encode logical qubits (i.e., exhibit a quantum memory), and even host chiral or non-modular topological order. We argue that a partial classification of imTO is given in terms of non-modular braided fusion categories.