Revisiting Nishimori multicriticality through the lens of information measures

TL;DR

This paper extends quantum information measures beyond the Nishimori line to serve as sharp indicators of phase transitions in quantum error correction models, providing precise estimates of critical points.

Contribution

It introduces generalized quantum information measures as phase transition indicators across the full parameter plane, with operational interpretations and exact inequalities.

Findings

Generalized measures attain extrema along the Nishimori line.

Coherent information shows minimal finite-size effects.

High-precision estimate of the Nishimori multicritical point: p_c=0.1092212(4).

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 $\pm J$ 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.