Sample complexity of fully self-consistent entanglement certification

Determine the sample complexity of self-consistent entanglement certification when the operational identities among the measurement effects are inferred from the same finite target-state data, including whether the effect complexity contributes to the required number of target-state copies.

Background

The paper establishes an optimal target-copy scaling of Θ_d(γ^{-2} log(1/δ)) only in the setting where the exact operational identities are supplied independently of the target-state data. In the fully self-consistent protocol, those identities must instead be inferred from finite observations of the same target-state copies used for certification.

Inference uncertainty changes the noncontextuality test because the experimentally estimated statistics need not satisfy the operational identities exactly. The unresolved issue is to develop a finite-copy analysis that incorporates uncertainty in the inferred identities and determines whether, and how, the number of distinct local effects required for a given entanglement resolution affects the total sample complexity. The paper identifies the cut-to-your-cloth and secondary-procedures techniques as possible frameworks for such an analysis.