Dated: February 1, 2024 | Kaixiang Su, Zhou Yang, Chao-Ming Jian
The paper explores the behavior of quantum error correction (QEC) codes under decoherence, focusing on the Rényi entropies $S_R$ of the error-corrupted mixed states. The authors construct statistical models that characterize these entropies for general Calderbank-Shor-Steane (CSS) codes decohered by bit-flip and phase-flip errors. They show that these models can be organized into a "tapestry of dualities," where pairs of statistical models with randomness (SM1 and SM2) are dual under a high-low-temperature (HLT) duality. For $R = 2, 3, \infty$, additional dualities (bit-phase-decoherence, BPD dualities) map between bit-flip and phase-flip errors. These dualities constrain the phase transitions and critical error rates in the decohered CSS codes. The paper also discusses the electric-magnetic symmetry in CSS codes, leading to self-dual error rates with super-universal properties. For general stabilizer codes decohered by generic Pauli noise, the authors construct statistical models and identify general dualities between different error rates. The results provide insights into the robustness of QEC codes against errors and the emergence of new out-of-equilibrium quantum phases.The paper explores the behavior of quantum error correction (QEC) codes under decoherence, focusing on the Rényi entropies $S_R$ of the error-corrupted mixed states. The authors construct statistical models that characterize these entropies for general Calderbank-Shor-Steane (CSS) codes decohered by bit-flip and phase-flip errors. They show that these models can be organized into a "tapestry of dualities," where pairs of statistical models with randomness (SM1 and SM2) are dual under a high-low-temperature (HLT) duality. For $R = 2, 3, \infty$, additional dualities (bit-phase-decoherence, BPD dualities) map between bit-flip and phase-flip errors. These dualities constrain the phase transitions and critical error rates in the decohered CSS codes. The paper also discusses the electric-magnetic symmetry in CSS codes, leading to self-dual error rates with super-universal properties. For general stabilizer codes decohered by generic Pauli noise, the authors construct statistical models and identify general dualities between different error rates. The results provide insights into the robustness of QEC codes against errors and the emergence of new out-of-equilibrium quantum phases.