Testing identity of collections of quantum states: sample complexity analysis

Marco Fanizza, Raffaele Salvia, Vittorio Giovannetti

Research output: Contribution to journalArticleResearchpeer-review


We study the problem of testing identity of a collection of unknown quantum states given sample access to this collection, each state appearing with some known probability. We show that for a collection of d-dimensional quantum states of cardinality N, the sample complexity is O(√Nd/ϵ2), with a matching lower bound, up to a multiplicative constant. The test is obtained by estimating the mean squared Hilbert-Schmidt distance between the states, thanks to a suitable generalization of the estimator of the Hilbert-Schmidt distance between two unknown states by Bădescu, O'Donnell, and Wright.

Original languageEnglish
Article numberA10
Number of pages29
Publication statusPublished - 11 Sept 2023


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