Intrinsic Mixed-state Topological Order

TL;DR

This paper introduces a new form of intrinsic mixed-state topological order arising from decoherence, characterized by long-range entanglement and nontrivial anyon statistics, demonstrated through models like the decohered Kitaev and double-semion models.

Contribution

It constructs explicit examples of mixed-state topological order induced by decoherence, revealing novel phases with nonbosonic anyons and new topological features absent in pure states.

Findings

Mixed states retain long-range entanglement despite destroyed quantum memory.

Decoherence can generate nonbosonic deconfined anyons with nontrivial braiding.

Certain mixed states cannot be prepared from separable states via finite-depth local channels.

Abstract

Decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. Here, we show that decoherence can also give rise to new types of topological order. Specifically, we construct concrete examples by proliferating fermionic anyons in the toric code via local quantum channels. The resulting mixed states retain long-range entanglement, which manifests in the nonzero topological entanglement negativity, though the topological quantum memory is destroyed by decoherence. By comparison with the gapless spin liquid in pure states, we show that the identified states represent a novel intrinsic mixed-state topological order, which has no counterpart in pure states. Through the lens of quantum anomalies of 1-form symmetries, we then provide general constructions of intrinsic mixed-state topological order and reveal the existence of nonbosonic deconfined anyons as another key feature of these novel phases. The extended meaning and characterization of deconfined excitations and their statistics in mixed states are clarified. Moreover, when these deconfined anyons have nontrivial braiding statistics, we prove that the mixed states cannot be prepared via finite-depth local quantum channels from any bipartite separable states. We further demonstrate our construction using the decohered Kitaev honeycomb model and the decohered double-semion model. In the latter case, a surprising scenario arises where decoherence gives rise to additional types of deconfined anyons.