[GS_C_QT]Optimal recovery for QEC / Rigorous results on mixed-state topological order
ABSTRACT
Abstract: I will present few related works. First, we discuss optimal recovery in quantum error correction, where the form of the recovery operation used to perform error-correction is optimised instead of a fixed (for example, measuring the stabilisers of a CSS code) beforehand. We state a fundamental upper bound on the fidelity of recovered states over all possible recovery channels, define optimal thresholds and optimal recovery schemes, and study their structurez [https://arxiv.org/pdf/2603.06520].
Next, I present upcoming joint work with Max McGinley, where we prove rigorous results on mixed-state topological order beyond Pauli stabilisers and Pauli errors, such as non-abelian codes under heralded erasure. By upper bounding the logical information leaked into the environment by a partition function of a stat-mech model called self-osculating walks [https://arxiv.org/pdf/2509.04568], we show that below a threshold, all the hallmarks of topological order can be shown to hold: (a) existence of thickened logical operators, (b) long-ranged mixed-state entanglement, (c) distinguishability of anyonic states, (d) recoverability of logical information.
