Testing identity of collections of quantum states: sample complexity analysis

Marco Fanizza; Raffaele Salvia; Vittorio Giovannetti

doi:10.22331/Q-2023-09-11-1105

Testing identity of collections of quantum states: sample complexity analysis

Marco Fanizza, Raffaele Salvia, Vittorio Giovannetti

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

Resumen

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.

Idioma original	Inglés
Número de artículo	A10
Número de páginas	29
Publicación	Quantum
Volumen	7
DOI	https://doi.org/10.22331/Q-2023-09-11-1105
Estado	Publicada - 11 sept 2023

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10.22331/Q-2023-09-11-1105Licencia: CC BY

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1 Terminado
1 Activo

DISCOVERY: Extracting information from quantum signals with nearterm programmable and self-calibrating quantum devices
Rosati , M. (Principal Investigator), Winter , A. J. (Investigador/a), Calsamiglia Costa, J. (Investigador/a), Winter , A. J. (Principal Investigator) & Rosati , M. (Investigador/a)
1/01/22 → 30/06/25
Proyecto: Proyecto Internacional de Investigación
QUANTUM: 001-P-001644, QUANTUM
Calsamiglia Costa, J. (Principal Investigator), Celi , A. (Investigador/a), Ahufinger Breto, V. (Investigador/a), Bagan Capella, E. (Investigador/a), Mompart Penina, J. (Investigador/a), Monteagudo Soldevilla, E. (Investigador/a), Muñoz Tapia, R. (Investigador/a), Oriols Pladevall, X. (Investigador/a), Sanpera Trigueros, A. (Investigador/a), Cartoixa Soler, X. (Investigador/a) & Garcia Diaz, M. (Investigador/a)
Departament d'Empresa i Coneixement (Generalitat de Catalunya)
1/01/19 → 30/06/22
Proyecto: Proyectos y Ayudas de Investigación

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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(√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 B{\u a}descu, O'Donnell, and Wright.",

author = "Marco Fanizza and Raffaele Salvia and Vittorio Giovannetti",

note = "Funding Information: M. F. thanks A. Montanaro for suggesting the problem, M. Rosati, M. Skotiniotis and J. Calsamiglia for many discussions about distance estimation, and M. Christandl, M. Hayashi and A. Winter for helpful comments. The authors acknowledge support by MIUR via PRIN 2017 (Progetto di Ricerca di Interesse Nazionale): project QUSHIP (2017SRNBRK). MF is supported by a Juan de la Cierva Formaci{\`o}n fellowship (project FJC2021-047404-I), with funding from MCIN/AEI/10.13039/501100011033 and European Union NextGenerationEU/PRTR, and by Spanish Agencia Estatal de Investigaci{\'o}n, project PID2019-107609GB-I00/AEI/10.13039/501100011033, by the European Union Regional Development Fund within the ERDF Operational Program of Catalunya (project QuantumCat, ref. 001-P-001644), and by European Space Agency, project ESA/ESTEC 2021-01250-ESA. Publisher Copyright: {\textcopyright} The Author(s) 2023.",

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doi = "10.22331/Q-2023-09-11-1105",

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Testing identity of collections of quantum states: sample complexity analysis

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Proyectos

DISCOVERY: Extracting information from quantum signals with nearterm programmable and self-calibrating quantum devices

QUANTUM: 001-P-001644, QUANTUM

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