On the optimal certification of von Neumann measurements

Abstract In this report we study certification of quantum measurements, which can be viewed as the extension of quantum hypotheses testing. This extension involves also the study of the input state and the measurement procedure. Here, we will be interested in two-point (binary) certification scheme...

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Autores principales:	Paulina Lewandowska, Aleksandra Krawiec, Ryszard Kukulski, Łukasz Pawela, Zbigniew Puchała
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/2c372f67dfc44ecd83ddb7dc59e1564f
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spelling	oai:doaj.org-article:2c372f67dfc44ecd83ddb7dc59e1564f2021-12-02T13:30:09ZOn the optimal certification of von Neumann measurements10.1038/s41598-021-81325-12045-2322https://doaj.org/article/2c372f67dfc44ecd83ddb7dc59e1564f2021-02-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-81325-1https://doaj.org/toc/2045-2322Abstract In this report we study certification of quantum measurements, which can be viewed as the extension of quantum hypotheses testing. This extension involves also the study of the input state and the measurement procedure. Here, we will be interested in two-point (binary) certification scheme in which the null and alternative hypotheses are single element sets. Our goal is to minimize the probability of the type II error given some fixed statistical significance. In this report, we begin with studying the two-point certification of pure quantum states and unitary channels to later use them to prove our main result, which is the certification of von Neumann measurements in single-shot and parallel scenarios. From our main result follow the conditions when two pure states, unitary operations and von Neumann measurements cannot be distinguished perfectly but still can be certified with a given statistical significance. Moreover, we show the connection between the certification of quantum channels or von Neumann measurements and the notion of q-numerical range.Paulina LewandowskaAleksandra KrawiecRyszard KukulskiŁukasz PawelaZbigniew PuchałaNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-16 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Paulina Lewandowska Aleksandra Krawiec Ryszard Kukulski Łukasz Pawela Zbigniew Puchała On the optimal certification of von Neumann measurements
description	Abstract In this report we study certification of quantum measurements, which can be viewed as the extension of quantum hypotheses testing. This extension involves also the study of the input state and the measurement procedure. Here, we will be interested in two-point (binary) certification scheme in which the null and alternative hypotheses are single element sets. Our goal is to minimize the probability of the type II error given some fixed statistical significance. In this report, we begin with studying the two-point certification of pure quantum states and unitary channels to later use them to prove our main result, which is the certification of von Neumann measurements in single-shot and parallel scenarios. From our main result follow the conditions when two pure states, unitary operations and von Neumann measurements cannot be distinguished perfectly but still can be certified with a given statistical significance. Moreover, we show the connection between the certification of quantum channels or von Neumann measurements and the notion of q-numerical range.
format	article
author	Paulina Lewandowska Aleksandra Krawiec Ryszard Kukulski Łukasz Pawela Zbigniew Puchała
author_facet	Paulina Lewandowska Aleksandra Krawiec Ryszard Kukulski Łukasz Pawela Zbigniew Puchała
author_sort	Paulina Lewandowska
title	On the optimal certification of von Neumann measurements
title_short	On the optimal certification of von Neumann measurements
title_full	On the optimal certification of von Neumann measurements
title_fullStr	On the optimal certification of von Neumann measurements
title_full_unstemmed	On the optimal certification of von Neumann measurements
title_sort	on the optimal certification of von neumann measurements
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/2c372f67dfc44ecd83ddb7dc59e1564f
work_keys_str_mv	AT paulinalewandowska ontheoptimalcertificationofvonneumannmeasurements AT aleksandrakrawiec ontheoptimalcertificationofvonneumannmeasurements AT ryszardkukulski ontheoptimalcertificationofvonneumannmeasurements AT łukaszpawela ontheoptimalcertificationofvonneumannmeasurements AT zbigniewpuchała ontheoptimalcertificationofvonneumannmeasurements
_version_	1718392965161811968

On the optimal certification of von Neumann measurements

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