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 general framework for quantum verification and certification in which the state produced in each round may depend arbitrarily on the preceding experimental history. Our method provides rigorous confidence intervals for observable expectation values averaged over the experimental trajectory. The framework covers both full verification, in which every state is measured, and spot-checking certification, in which a randomly selected subset is tested to certify the average observable value of the complementary, remaining systems. We apply the framework to importance-sampled Pauli measurements for direct fidelity estimation, energy estimation, and entanglement witnessing, and to classical shadows, allowing multiple observables to be certified simultaneously from the same test data. We illustrate the framework numerically and demonstrate it experimentally through Bell-state certification on a quantum processor.
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BibTeX
@misc{navarro2026certifying,
title = {{Certifying quantum states without independence assumptions}},
author = {Mariana Navarro and Leonardo Zambrano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.31913},
eprint = {2606.31913},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.31913},
}
RIS
TY - UNPB
TI - Certifying quantum states without independence assumptions
AU - Mariana Navarro
AU - Leonardo Zambrano
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2606.31913
UR - https://arxiv.org/abs/2606.31913
AB - 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 general framework for quantum verification and certification in which the state produced in each round may depend arbitrarily on the preceding experimental history. Our method provides rigorous confidence intervals for observable expectation values averaged over the experimental trajectory. The framework covers both full verification, in which every state is measured, and spot-checking certification, in which a randomly selected subset is tested to certify the average observable value of the complementary, remaining systems. We apply the framework to importance-sampled Pauli measurements for direct fidelity estimation, energy estimation, and entanglement witnessing, and to classical shadows, allowing multiple observables to be certified simultaneously from the same test data. We illustrate the framework numerically and demonstrate it experimentally through Bell-state certification on a quantum processor.
ER -