An efficient method for spot-checking quantum properties with sequential trials

TL;DR

This paper introduces an efficient method for certifying quantum properties through sequential, non-i.i.d. trials, ensuring reliable performance estimates with minimal spot-checking even in complex, practical quantum scenarios.

Contribution

The authors develop a novel certification method applicable to non-i.i.d. quantum trials that is efficient with finite data and asymptotically tight, requiring only a constant number of spot-checks on average.

Findings

Method works efficiently with finite trials

Provides asymptotically tight performance certificates

Requires only a constant number of spot-checks asymptotically

Abstract

In practical situations, the reliability of quantum resources can be compromised due to complex generation processes or adversarial manipulations during transmission. Consequently, the trials generated sequentially in an experiment may exhibit non-independent and non-identically distributed (non-i.i.d.) behavior. This non-i.i.d. behavior can introduce security concerns and result in faulty estimates when performing information tasks such as quantum key distribution, self-testing, verifiable quantum computation, and resource allocation in quantum networks. To certify the performance of such tasks, one can make a random decision in each trial, either spot-checking some desired property or utilizing the quantum resource for the given task. However, a general method for certification with a sequence of non-i.i.d. spot-checking trials is still missing. Here, we develop such a method. This method not only works efficiently with a finite number of trials but also yields asymptotically tight certificates of performance. Our analysis shows that even as the total number of trials approaches infinity, only a constant number of trials needs to be spot-checked on average to certify the average performance of the remaining trials at a specified confidence level.