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We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits.
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2009
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M. B. Hastings, Topological order at nonzero temperature, Physical review letters 107
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I. H. Kim, Long-range entanglement is necessary for a topological storage of quantum information, Physical review letters 111
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M. Junge, R. Renner, D. Sutter, M. M. Wilde, and A. Winter, Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy, Annales Henri Poincaré 19
2018
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A. Coser and D. Pérez-García, Classification of phases for mixed states via fast dissipative evolution, Quantum 3
2019
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2019
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T.-C. Lu, T. H. Hsieh, and T. Grover, Detecting topological order at finite temperature using entanglement negativity, Phys. Rev. Lett. 125
2020
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B. Shi, K. Kato, and I. H. Kim, Fusion rules from entanglement, Annals of Physics 418
2020
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2022
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C. de Groot, A. Turzillo, and N. Schuch, Symmetry protected topological order in open quantum systems, Quantum 6
2022
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2023
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Y. Zou, S. Sang, and T. H. Hsieh, Channeling quantum criticality, Physical Review Letters 130
2023
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T.-C. Lu, Z. Zhang, S. Vijay, and T. H. Hsieh, Mixed-state long-range order and criticality from measurement and feedback, PRX Quantum 4
2024
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S. Sang, Y. Zou, and T. H. Hsieh, Mixed-state quantum phases: Renormalization and quantum error correction, Phys. Rev. X 14
2024
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T. Rakovszky, S. Gopalakrishnan, and C. von Keyserlingk, Defining stable phases of open quantum systems, Phys. Rev. X 14
2024
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P. Sala, S. Gopalakrishnan, M. Oshikawa, and Y. You, Spontaneous strong symmetry breaking in open systems: Purification perspective, Physical Review B 110
2024
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2023
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G.-Y. Zhu, N. Tantivasadakarn, A. Vishwanath, S. Trebst, and R. Verresen, Nishimori’s cat: Stable long-range entanglement from finite-depth unitaries and weak measurements, Phys. Rev. Lett. 131
2023
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R. Ma and C. Wang, Average symmetry-protected topological phases, Physical Review X 13
2023
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2023
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2023
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S. Sang, Z. Li, T. H. Hsieh, and B. Yoshida, Ultrafast entanglement dynamics in monitored quantum circuits, PRX Quantum 4
2023
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2023
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2024
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2024
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M. Levin, A physical proof of the topological entanglement entropy inequality (2024)
2024
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2025
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2025
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S. Sang and T. H. Hsieh, Stability of mixed-state quantum phases via finite markov length, Phys. Rev. Lett. 134
2025
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2025
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C. Zhang, Y. Xu, J.-H. Zhang, C. Xu, Z. Bi, and Z.-X. Luo, Strong-to-weak spontaneous breaking of 1-form symmetry and intrinsically mixed topological order, Phys. Rev. B 111
2025
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2025
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J. Y. Lee, Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold, Physical Review Letters 134
2025
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B. Placke, V. Khemani, and T. Rakovszky, Emergent symmetries in open quantum systems, to be appeared (2025)
2025
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