Intrinsic mixed-state topological order without quantum memory

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 two such examples by proliferating fermionic anyons in the two-dimensional toric code model and the Kitaev honeycomb model through certain 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. We argue that these properties are stable against perturbations. Therefore, the identified states represent a novel intrinsic mixed-state quantum topological order, which has no counterpart in pure states.