A Note on Parallel Distinguishability of two Quantum Operations

A Note on Parallel Distinguishability of two Quantum Operations

We consider a homogeneous system of linear equations of the form \(A_\alpha^{\otimes N} {\bf x} = 0\) arising from the distinguishability of two quantum operations by \(N\) uses in parallel, where the coefficient matrix \(A_\alpha\) depends on a real parameter \(\alpha\). It was conjectured by Duan...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2020-03
Hauptverfasser: Chi-Kwong, Li, Liu, Yue, Ma, Chao, Pelejo, Diane Christine P
Format: Artikel
Sprache:eng
Schlagworte:
Linear equations
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Chi-Kwong, Li
Liu, Yue
Ma, Chao
Pelejo, Diane Christine P
description We consider a homogeneous system of linear equations of the form \(A_\alpha^{\otimes N} {\bf x} = 0\) arising from the distinguishability of two quantum operations by \(N\) uses in parallel, where the coefficient matrix \(A_\alpha\) depends on a real parameter \(\alpha\). It was conjectured by Duan et al. that the system has a non-trivial nonnegative solution if and only if \(\alpha\) lies in a certain interval \(R_N\) depending on \(N\). We affirm the necessity part of the conjecture and establish the sufficiency of the conjecture for \(N\leq 10\) by presenting explicit non-trivial nonnegative solutions for the linear system.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2241819844</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2241819844</sourcerecordid><originalsourceid>FETCH-proquest_journals_22418198443</originalsourceid><addsrcrecordid>eNqNyrsKwjAUgOEgCBbtOxxwLrRJqnES8YKTF3AvEVJNiTk1OUF8ex18AKd_-P4By7gQVaEk5yOWx9iVZclnc17XImPLFRyQDKCHkw7aOeNgYyNZf0s23vXVOktvwBbohXBO2lN6wLE3QZNFHyds2GoXTf7rmE1328t6X_QBn8lEajpMwX-p4VxWqlooKcV_1wfirDiy</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2241819844</pqid></control><display><type>article</type><title>A Note on Parallel Distinguishability of two Quantum Operations</title><source>Free E- Journals</source><creator>Chi-Kwong, Li ; Liu, Yue ; Ma, Chao ; Pelejo, Diane Christine P</creator><creatorcontrib>Chi-Kwong, Li ; Liu, Yue ; Ma, Chao ; Pelejo, Diane Christine P</creatorcontrib><description>We consider a homogeneous system of linear equations of the form \(A_\alpha^{\otimes N} {\bf x} = 0\) arising from the distinguishability of two quantum operations by \(N\) uses in parallel, where the coefficient matrix \(A_\alpha\) depends on a real parameter \(\alpha\). It was conjectured by Duan et al. that the system has a non-trivial nonnegative solution if and only if \(\alpha\) lies in a certain interval \(R_N\) depending on \(N\). We affirm the necessity part of the conjecture and establish the sufficiency of the conjecture for \(N\leq 10\) by presenting explicit non-trivial nonnegative solutions for the linear system.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Linear equations</subject><ispartof>arXiv.org, 2020-03</ispartof><rights>2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>777,781</link.rule.ids></links><search><creatorcontrib>Chi-Kwong, Li</creatorcontrib><creatorcontrib>Liu, Yue</creatorcontrib><creatorcontrib>Ma, Chao</creatorcontrib><creatorcontrib>Pelejo, Diane Christine P</creatorcontrib><title>A Note on Parallel Distinguishability of two Quantum Operations</title><title>arXiv.org</title><description>We consider a homogeneous system of linear equations of the form \(A_\alpha^{\otimes N} {\bf x} = 0\) arising from the distinguishability of two quantum operations by \(N\) uses in parallel, where the coefficient matrix \(A_\alpha\) depends on a real parameter \(\alpha\). It was conjectured by Duan et al. that the system has a non-trivial nonnegative solution if and only if \(\alpha\) lies in a certain interval \(R_N\) depending on \(N\). We affirm the necessity part of the conjecture and establish the sufficiency of the conjecture for \(N\leq 10\) by presenting explicit non-trivial nonnegative solutions for the linear system.</description><subject>Linear equations</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNyrsKwjAUgOEgCBbtOxxwLrRJqnES8YKTF3AvEVJNiTk1OUF8ex18AKd_-P4By7gQVaEk5yOWx9iVZclnc17XImPLFRyQDKCHkw7aOeNgYyNZf0s23vXVOktvwBbohXBO2lN6wLE3QZNFHyds2GoXTf7rmE1328t6X_QBn8lEajpMwX-p4VxWqlooKcV_1wfirDiy</recordid><startdate>20200304</startdate><enddate>20200304</enddate><creator>Chi-Kwong, Li</creator><creator>Liu, Yue</creator><creator>Ma, Chao</creator><creator>Pelejo, Diane Christine P</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20200304</creationdate><title>A Note on Parallel Distinguishability of two Quantum Operations</title><author>Chi-Kwong, Li ; Liu, Yue ; Ma, Chao ; Pelejo, Diane Christine P</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_22418198443</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Linear equations</topic><toplevel>online_resources</toplevel><creatorcontrib>Chi-Kwong, Li</creatorcontrib><creatorcontrib>Liu, Yue</creatorcontrib><creatorcontrib>Ma, Chao</creatorcontrib><creatorcontrib>Pelejo, Diane Christine P</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chi-Kwong, Li</au><au>Liu, Yue</au><au>Ma, Chao</au><au>Pelejo, Diane Christine P</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>A Note on Parallel Distinguishability of two Quantum Operations</atitle><jtitle>arXiv.org</jtitle><date>2020-03-04</date><risdate>2020</risdate><eissn>2331-8422</eissn><abstract>We consider a homogeneous system of linear equations of the form \(A_\alpha^{\otimes N} {\bf x} = 0\) arising from the distinguishability of two quantum operations by \(N\) uses in parallel, where the coefficient matrix \(A_\alpha\) depends on a real parameter \(\alpha\). It was conjectured by Duan et al. that the system has a non-trivial nonnegative solution if and only if \(\alpha\) lies in a certain interval \(R_N\) depending on \(N\). We affirm the necessity part of the conjecture and establish the sufficiency of the conjecture for \(N\leq 10\) by presenting explicit non-trivial nonnegative solutions for the linear system.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2020-03
issn 2331-8422
language eng
recordid cdi_proquest_journals_2241819844
source Free E- Journals
subjects Linear equations
title A Note on Parallel Distinguishability of two Quantum Operations
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-19T23%3A41%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=A%20Note%20on%20Parallel%20Distinguishability%20of%20two%20Quantum%20Operations&rft.jtitle=arXiv.org&rft.au=Chi-Kwong,%20Li&rft.date=2020-03-04&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2241819844%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2241819844&rft_id=info:pmid/&rfr_iscdi=true