Emanuel Knill

The reliability of quantum resources can be compromised in practice due to the complexity of their generation processes and/or the potential manipulations by untrusted parties during transmission. When performing an information task with an unreliable quantum resource, it is incorrect to treat the random variables associated with repeated experimental trials as independent and identically distributed (i.i.d.). To certify the performance of such a task, one can make a random decision in each trial, either to spot-check some property of the quantum resource or to utilize the resource for the task. The task considered can be quantum key distribution, quantum randomness expansion, verifiable quantum computation, or resource allocation in quantum networks. Unfortunately, existing methods for certifying quantum performance through spot-checking are not suitable for non-i.i.d. repeated trials without additional assumptions. Here we present a novel method to address this challenge. The method works efficiently with a finite number of non-i.i.d. trials. Furthermore, our method can be adapted to estimate quantum properties in situations where the quantum resource is spot-checked and destroyed by a measurement during each non-i.i.d. repeated trial.