Optimal cloning channel for stabilizer states

Identify the optimal cloning channel for the family of stabilizer states on $n$ qubits and determine the unsettled prefactors and subleading terms in its optimal sample complexity.

Background

The paper notes that stabilizer states admit a measure-and-prepare cloning strategy with asymptotically optimal constant-error sample complexity, and that matching linear lower bounds are known. Nevertheless, asymptotic scaling alone does not determine the optimal channel or the finite-size complexity.

The authors explicitly state that the prefactors and subleading terms remain unsettled and that the optimal stabilizer-state cloning channel is unknown.

References

However, the prefactors and subleading terms of this optimal complexity are not settled, and the optimal cloning channel for stabilizer states remains an open question.

— Approximate cloning of structured pure states  (2610.06723 - Herasymenko et al., 5 Oct 2026) in Section 4, subsection “Cloning and learning for continuous families”