Local certification of unitary operations

Fuente: arXiv
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Autori principali: Kukulski, Ryszard, Stępniak, Mateusz, Hendzel, Kamil, Pawela, Łukasz, Gardas, Bartłomiej, Puchała, Zbigniew
Natura: Preprint
Pubblicazione: 2023
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author Kukulski, Ryszard
Stępniak, Mateusz
Hendzel, Kamil
Pawela, Łukasz
Gardas, Bartłomiej
Puchała, Zbigniew
author_facet Kukulski, Ryszard
Stępniak, Mateusz
Hendzel, Kamil
Pawela, Łukasz
Gardas, Bartłomiej
Puchała, Zbigniew
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2312_17037
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Local certification of unitary operations
Kukulski, Ryszard
Stępniak, Mateusz
Hendzel, Kamil
Pawela, Łukasz
Gardas, Bartłomiej
Puchała, Zbigniew
Quantum Physics
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.
title Local certification of unitary operations
topic Quantum Physics
url https://arxiv.org/abs/2312.17037