Optimal leading constant for adaptive single-copy learning

Determine whether adaptive single-copy measurements can learn an arbitrary n-qubit stabilizer state using n+o(n) copies at fixed failure probability, or prove that the single-copy restriction necessarily imposes a leading constant strictly greater than one.

Background

The exact-learning algorithm uses 4n+O(sqrt(n)) copies for fixed failure probability, whereas arbitrary collective measurements achieve n+O(1) copies with a matching leading-order lower bound.

The open question concerns whether adaptivity can close not only the asymptotic scaling gap but also the leading-order sample-complexity gap between single-copy and collective measurement models.

References

Can adaptive single-copy measurements also achieve $n+o(n)$ copies, or does the single-copy restriction impose a strictly larger leading constant?

— Adaptivity is all you need: Optimal stabilizer learning using just single-copy measurements  (2610.02031 - Bittel et al., 1 Oct 2026) in Section Conclusions and open questions, item “The optimal leading constant”