Asymptotically optimal overhead and protocols for magic state distillation

Characterize the optimal asymptotic overhead achievable for magic state distillation and identify the corresponding asymptotically optimal family of protocols that attain this overhead.

Background

The paper establishes the achievability of constant-overhead magic state distillation, showing a nonzero asymptotic rate, but does not settle optimality of the overhead among all possible protocols.

Determining the fundamental limits and matching constructions is a central open problem in the resource theory of magic and fault-tolerant quantum computation.