Stability of mixed-state quantum phases via finite Markov length

          @misc{ pirsa_PIRSA:24050029,
            doi = {10.48660/24050029},
            url = {https://pirsa.org/24050029},
            author = {Sang, Shengqi},
            keywords = {Quantum Information},
            language = {en},
            title = {Stability of mixed-state quantum phases via finite Markov length},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050029 see, \url{https://pirsa.org}}
          }
          

Abstract

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. In this talk we introduce 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. This implies that the mixed state phase transition coincides with the decodability transition and also suggests a quasi-local decoding channel.