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  • Open Access

Revisiting Nishimori multicriticality through the lens of information measures

Zhou-Quan Wan1,*, Xu-Dong Dai2,*, and Guo-Yi Zhu3,†

  • *These authors contributed equally to this work.
  • †Contact author: guoyizhu@hkust-gz.edu.cn
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Phys. Rev. Research 8, 023059 – Published 17 April, 2026

DOI: https://doi.org/10.1103/b8y5-k3y6

Abstract

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 ±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 pc=0.1092212(4) and the associated critical exponents.

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Phys. Rev. Research 8, 023059– Published 17 April, 2026
  • Received 8 December 2025
  • Accepted 27 March 2026
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