  For quantum phases of Hamiltonian ground states, the energy gap plays a
central role in ensuring the stability of the phase as long as the gap remains
finite. We propose Markov length, the length scale at which the quantum
conditional mutual information (CMI) decays exponentially, as an equally
essential quantity characterizing mixed-state phases and transitions. For a
state evolving under a local Lindbladian, we argue that if its Markov length
remains finite along the evolution, then it remains in the same phase, meaning
there exists another quasi-local Lindbladian evolution that can reverse the
former one. We apply this diagnostic to toric code subject to decoherence and
show that the Markov length is finite everywhere except at its decodability
transition, at which it diverges. CMI in this case can be mapped to the free
energy cost of point defects in the random bond Ising model. This implies that
the mixed state phase transition coincides with the decodability transition and
also suggests a quasi-local decoding channel.
