Divergence of the Markov length at the decoding transition

Determine whether the Markov length diverges near the decoding transition between the weak-noise and strong-noise regimes for noisy quantum low-density parity-check code states.

Background

The paper proves exponential decay of conditional mutual information in two complementary noise regimes: weak noise, where error clusters are unlikely to cross the buffer, and strong noise, where the buffer retains little information. These regimes lie on opposite sides of a decoding transition, while the intermediate region is not controlled by the presented bounds. The Markov length measures the characteristic buffer width over which conditional mutual information decays, so determining whether it diverges near the transition would clarify the relationship between mixed-state conditional-independence structure and decoding criticality.