Revisiting Nishimori multicriticality through the lens of information measures
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908974469611520 |
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| author | Wan, Zhou-Quan Dai, Xu-Dong Zhu, Guo-Yi |
| author_facet | Wan, Zhou-Quan Dai, Xu-Dong Zhu, Guo-Yi |
| contents | The quantum error correction threshold is closely related to the Nishimori physics of random statistical models. We extend quantum information measures such as coherent information beyond the Nishimori line and establish them as sharp indicators of phase transitions over the full $p$-$T$ plane. These generalized measures admit a natural operational interpretation as diagnostics of inference mismatch for decoders operating at an effective temperature. We derive exact inequalities for several generalized measures, demonstrating that each attains its extremum along the Nishimori line. As a direct application, we study these measures in the 2d $\pm J$ random-bond Ising model-corresponding to a surface code under bit-flip noise-and revisit the Nishimori multicritical point. Among all indicators, coherent information exhibits the weakest finite-size effects, enabling a high-precision estimate $p_c=0.1092212(4)$ and the associated critical exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Nishimori multicriticality through the lens of information measures Wan, Zhou-Quan Dai, Xu-Dong Zhu, Guo-Yi Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Quantum Physics The quantum error correction threshold is closely related to the Nishimori physics of random statistical models. We extend quantum information measures such as coherent information beyond the Nishimori line and establish them as sharp indicators of phase transitions over the full $p$-$T$ plane. These generalized measures admit a natural operational interpretation as diagnostics of inference mismatch for decoders operating at an effective temperature. We derive exact inequalities for several generalized measures, demonstrating that each attains its extremum along the Nishimori line. As a direct application, we study these measures in the 2d $\pm J$ random-bond Ising model-corresponding to a surface code under bit-flip noise-and revisit the Nishimori multicritical point. Among all indicators, coherent information exhibits the weakest finite-size effects, enabling a high-precision estimate $p_c=0.1092212(4)$ and the associated critical exponents. |
| title | Revisiting Nishimori multicriticality through the lens of information measures |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2511.02907 |