Certifying quantum states without independence assumptions

Abstract

Standard quantum verification and certification protocols often assume that experimental sources emit independent and identically distributed (i.i.d.) states. In realistic scenarios, however, temporal drift, memory effects, feedback, and correlated noise can violate this assumption, causing standard analyses to underestimate uncertainty and overestimate device performance. Here, we introduce a framework for quantum verification and certification that remains valid without independence assumptions. Our method gives rigorous confidence intervals for the time-averaged expectation value of any fixed observable, even when each prepared state may depend on the previous experimental history. For full verification, we recover the standard i.i.d. sample-complexity scaling. For certification, we develop a spot-checking protocol that randomly selects a subset of states to certify an average target property of the remaining states, which are used for a parallel quantum task. We demonstrate the framework numerically for energy estimation and entanglement witnessing under drift, and experimentally for Bell-state certification on a quantum processor.