Theory of versatile fidelity estimation with confidence

Abstract

Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the experimentalist to choose a convenient measurement setting. Our primary focus lies on a method that constructs an estimator with nearly minimax optimal confidence interval for any specified measurement setting. We demonstrate, through a combination of theoretical and numerical results, various desirable properties for the method: robustness against experimental imperfections, competitive sample complexity, and accurate estimates in practice. We compare this method with Maximum Likelihood Estimation and the associated Profile Likelihood method, a Semi-Definite Programming based approach, as well as a popular direct fidelity estimation technique.

Verification of arbitrary entangled states with homogeneous local measurements

“…Exemption of the completeness constraint enables our method to give a local measurement protocol for arbitrary estimation tasks, which is comparable to the optimal one. Recently, a method called versatile fidelity estimation [48,49] has used a different statistical method that gives the same order of sampling complexity such that the optimal measurement is {|ψ ψ|, 1 1 − |ψ ψ|}, which can be relaxed to {Ω Hom , 1 1 − Ω Hom }. Moreover, our extended discussions cover the results of direct fidelity estimation [14], which gives the same measurement protocol for stabilizer states using only Pauli projections.…”