Certification of quantum properties with imperfect measurements

TL;DR

This paper introduces a robust certification method for quantum states that accounts for measurement imperfections and shot noise, enabling reliable validation of quantum properties in experimental settings.

Contribution

It extends existing certification techniques by incorporating measurement imperfections and statistical noise, providing explicit bounds and a convex optimization framework.

Findings

The method effectively accounts for both shot noise and measurement errors.

It provides explicit bounds on quantum function values considering imperfections.

The approach enhances robustness of quantum state certification in experiments.

Abstract

The accurate characterization of quantum systems is essential for the advancement of quantum technologies. In particular, certifying convex functions of quantum states plays a central role in many applications. We present a certification method for experimentally prepared quantum states that accounts for both shot noise and measurement imperfections in the data-acquisition stage. Building upon previous work, our method extends confidence regions to accommodate imperfect control over measurements. The values of the functions can then be bounded using convex optimization techniques. We provide explicit prescriptions for quantifying the noise contribution from finite statistics and for estimating the effect of measurement imperfections. By jointly incorporating statistical and systematic errors, the method yields a robust certification framework for quantum experiments.