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Stability of Mixed-State Quantum Phases via Finite Markov Length
Shengqi Sang1,2,3, Timothy H Hsieh1
1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Physical Review Letters
|March 7, 2025
Summary
We introduce Markov length to characterize mixed-state phases. Finite Markov length indicates phase stability under local Lindbladian evolution, with divergence signaling phase transitions.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
Background:
- The energy gap is crucial for the stability of Hamiltonian ground states.
- Characterizing mixed-state phases and their transitions requires new theoretical tools.
Purpose of the Study:
- To propose Markov length as a key diagnostic for mixed-state phases and transitions.
- To investigate the behavior of Markov length in decohered quantum systems.
Main Methods:
- Defining Markov length as the decay scale of quantum conditional mutual information (CMI).
- Analyzing the evolution of Markov length under local Lindbladian dynamics.
- Applying the Markov length diagnostic to the toric code model under decoherence.
Main Results:
- Markov length characterizes mixed-state phases; finite length implies phase stability.
- For the decohered toric code, Markov length diverges at the decodability transition.
- CMI at the transition maps to free energy of defects in the random bond Ising model.
Conclusions:
- Mixed-state phase transitions coincide with decodability transitions.
- Markov length provides a new framework for understanding phase transitions in open quantum systems.
- The findings suggest the existence of quasilocal decoding channels.
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