Optimality of the eight-copy protocol

Determine whether the universal eight-copy exact magic-state concentration protocol for converting eight copies of an unknown pure non-stabilizer qubit state into an exact CCZ state achieves the optimal success probability among all universal stabilizer protocols acting on eight input copies.

Background

The paper constructs a universal eight-copy stabilizer protocol that converts eight copies of an arbitrary unknown pure non-stabilizer qubit state into an exact CCZ magic state with success probability proportional to the linearized order-three stabilizer Rényi entropy. In contrast to the six-copy protocol, whose success probability is proved optimal, the eight-copy construction is accompanied only by an upper bound that applies to arbitrary fixed non-stabilizer targets and does not establish equality for the CCZ target.

Resolving this problem would determine whether the improved eight-copy success probability is globally optimal or whether a different universal stabilizer protocol can achieve a higher success probability. The question is relevant both to finite-copy universal magic-state concentration and to the asymptotic rates obtained by repeating the eight-copy protocol.