  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 to the
gapless spin liquid in pure states, we show that the identified states
represent a novel intrinsic mixed-state quantum 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
quantum topological order, and reveal the existence of non-bosonic 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 %must be bipartite long-range
entangled for any bipartition. That is, such 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.
