Local certification of unitary operations

Abstract In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the...

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Main Authors: Ryszard Kukulski, Mateusz Stępniak, Kamil Hendzel, Łukasz Pawela, Bartłomiej Gardas, Zbigniew Puchała
Format: Article
Language:English
Published: Nature Portfolio 2024-11-01
Series:Scientific Reports
Online Access:https://doi.org/10.1038/s41598-024-75148-z
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author Ryszard Kukulski
Mateusz Stępniak
Kamil Hendzel
Łukasz Pawela
Bartłomiej Gardas
Zbigniew Puchała
author_facet Ryszard Kukulski
Mateusz Stępniak
Kamil Hendzel
Łukasz Pawela
Bartłomiej Gardas
Zbigniew Puchała
author_sort Ryszard Kukulski
collection DOAJ
description Abstract In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement with auxiliary systems. Our result indicates connection of the local certification problem with a product numerical range of unitary matrices. We show that the optimal local strategy does not need usage of auxiliary systems and requires only single round of one-way classical communication. Moreover, we compare local and global certification strategies and show that typically local strategies are optimal, yet in some extremal cases, where global strategies make no errors, local ones may fail miserably. Finally, some application for local certification of von Neumann measurements are discussed as well.
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institution Kabale University
issn 2045-2322
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publishDate 2024-11-01
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spelling doaj-art-4a19bf4b3dfb46509e517c06b42c70de2024-11-10T12:23:04ZengNature PortfolioScientific Reports2045-23222024-11-011411810.1038/s41598-024-75148-zLocal certification of unitary operationsRyszard Kukulski0Mateusz Stępniak1Kamil Hendzel2Łukasz Pawela3Bartłomiej Gardas4Zbigniew Puchała5Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian UniversityQuantumz.io Sp. z o.o.Quantumz.io Sp. z o.o.Institute of Theoretical and Applied Informatics, Polish Academy of SciencesInstitute of Theoretical and Applied Informatics, Polish Academy of SciencesInstitute of Theoretical and Applied Informatics, Polish Academy of SciencesAbstract In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement with auxiliary systems. Our result indicates connection of the local certification problem with a product numerical range of unitary matrices. We show that the optimal local strategy does not need usage of auxiliary systems and requires only single round of one-way classical communication. Moreover, we compare local and global certification strategies and show that typically local strategies are optimal, yet in some extremal cases, where global strategies make no errors, local ones may fail miserably. Finally, some application for local certification of von Neumann measurements are discussed as well.https://doi.org/10.1038/s41598-024-75148-z
spellingShingle Ryszard Kukulski
Mateusz Stępniak
Kamil Hendzel
Łukasz Pawela
Bartłomiej Gardas
Zbigniew Puchała
Local certification of unitary operations
Scientific Reports
title Local certification of unitary operations
title_full Local certification of unitary operations
title_fullStr Local certification of unitary operations
title_full_unstemmed Local certification of unitary operations
title_short Local certification of unitary operations
title_sort local certification of unitary operations
url https://doi.org/10.1038/s41598-024-75148-z
work_keys_str_mv AT ryszardkukulski localcertificationofunitaryoperations
AT mateuszstepniak localcertificationofunitaryoperations
AT kamilhendzel localcertificationofunitaryoperations
AT łukaszpawela localcertificationofunitaryoperations
AT bartłomiejgardas localcertificationofunitaryoperations
AT zbigniewpuchała localcertificationofunitaryoperations