Equivalence of single-shot correction and self-correction

Determine whether single-shot quantum error correction is equivalent to self-correction or is strictly stronger for quantum low-density parity-check codes.

Background

The paper proves that single-shot quantum error correction implies self-correction and notes that this implication also holds for arbitrary stabilizer codes under the stated framework. It compares this result with prior empirical evidence and related constructions suggesting that the two properties are closely connected for QLDPC codes.

A formal converse—whether self-correction implies single-shot correction—and, more broadly, whether the two properties are equivalent or whether single-shot correction is strictly stronger, is not established in the paper.

References

In light of our simple yet general proof that single-shot implies self-correction, can the converse be proven in a general manner (say, for any QLDPC code)? Indeed, Bombin has given an empirical analysis showing that the two are closely related when dealing with QLDPC codes with sparse meta-checks. This manuscript, in conjunction of , shows that even when meta-checks are non-sparse, the two properties can still closely related. However, neither has shown a formal equivalence between the two properties, and thus begs the question whether single-shot is equal to or strictly stronger than self-correction?

— One-Shot any Code  (2610.02137 - Yuan, 1 Oct 2026) in Section 1, Outlook