Related papers: Testing identity of collections of quantum states: sample complexity analysis

Testing identity of collections of quantum states: sample complexity analysis

URL: http://arxiv.org/abs/2103.14511v5
Date: Thu, 7 Sep 2023 17:06:27 GMT
Title: Testing identity of collections of quantum states: sample complexity analysis
Authors: Marco Fanizza, Raffaele Salvia, Vittorio Giovannetti
Abstract summary: We show that for a collection of $d$-dimensional quantum states of cardinality $N$, the sample complexity is $O(sqrtNd/epsilon2)$. The test is obtained by estimating the mean squared-Schmidt distance between the states.
Score: 1.227734309612871
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
Abstract: 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 $O(\sqrt{N}d/\epsilon^2)$, {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 B\u{a}descu, O'Donnell, and Wright (https://dl.acm.org/doi/10.1145/3313276.3316344).

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