Fidelity Estimation of Entangled Measurements with Local States

Abstract

We propose an efficient protocol to estimate the fidelity of an $n$-qubit entangled measurement device, requiring only qubit state preparations and classical data post-processing. It works by measuring the eigenstates of Pauli operators, which are strategically selected according to their importance weights and collectively contributed by all measurement operators. We rigorously analyze the protocol's performance and demonstrate that its sample complexity is uniquely determined by the number of Pauli operators possessing non-zero expectation values with respect to the target measurement. Moreover, from a resource-theoretic perspective, we introduce the stabilizer R\'enyi entropy of quantum measurements as a precise metric to quantify the inherent difficulty of estimating measurement fidelity.