<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03123361</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-20T23:23:13+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">On-State Commutativity of Measurements and Joint Distributions of Their Outcomes</title>
            <author role="aut">
              <persName>
                <forename type="first">Jan</forename>
                <surname>Czajkowski</surname>
              </persName>
              <idno type="halauthorid">2139364-0</idno>
              <affiliation ref="#struct-120654"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Alex</forename>
                <surname>Grilo</surname>
              </persName>
              <email type="md5">5ac5c0983ebe805dc5dc53139404e804</email>
              <email type="domain">proton.me</email>
              <idno type="idhal" notation="string">abgrilo</idno>
              <idno type="idhal" notation="numeric">740595</idno>
              <idno type="halauthorid" notation="string">2045927-740595</idno>
              <idno type="VIAF">https://viaf.org/viaf/40156251695707990603</idno>
              <idno type="IDREF">https://www.idref.fr/236329286</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-7374-7082</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/GCR-4553-2022</idno>
              <affiliation ref="#struct-541726"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Alex</forename>
                <surname>Bredariol Grilo</surname>
              </persName>
              <email type="md5">5ac5c0983ebe805dc5dc53139404e804</email>
              <email type="domain">proton.me</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2021-01-27 18:00:56</date>
              <date type="whenModified">2025-07-10 16:10:04</date>
              <date type="whenReleased">2021-01-27 18:00:56</date>
              <date type="whenProduced">2021-01-27</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/2101.08313"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="379309">
                <persName>
                  <forename>Alex</forename>
                  <surname>Bredariol Grilo</surname>
                </persName>
                <email type="md5">5ac5c0983ebe805dc5dc53139404e804</email>
                <email type="domain">proton.me</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03123361</idno>
            <idno type="halUri">https://hal.science/hal-03123361</idno>
            <idno type="halBibtex">czajkowski:hal-03123361</idno>
            <idno type="halRefHtml">2021</idno>
            <idno type="halRef">2021</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="LIP6" corresp="SORBONNE-UNIVERSITE">Laboratoire d'Informatique de Paris 6</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SORBONNE-UNIV" corresp="SORBONNE-UNIVERSITE">Sorbonne Université 01/01/2018</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="TEST-HALCNRS">Collection test HAL CNRS</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="SUPRA_MATHS_INFO">Mathématiques + Informatique</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">On-State Commutativity of Measurements and Joint Distributions of Their Outcomes</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Jan</forename>
                    <surname>Czajkowski</surname>
                  </persName>
                  <idno type="halauthorid">2139364-0</idno>
                  <affiliation ref="#struct-120654"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Alex</forename>
                    <surname>Grilo</surname>
                  </persName>
                  <email type="md5">5ac5c0983ebe805dc5dc53139404e804</email>
                  <email type="domain">proton.me</email>
                  <idno type="idhal" notation="string">abgrilo</idno>
                  <idno type="idhal" notation="numeric">740595</idno>
                  <idno type="halauthorid" notation="string">2045927-740595</idno>
                  <idno type="VIAF">https://viaf.org/viaf/40156251695707990603</idno>
                  <idno type="IDREF">https://www.idref.fr/236329286</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-7374-7082</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/GCR-4553-2022</idno>
                  <affiliation ref="#struct-541726"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">2101.08313</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="phys.qphy">Physics [physics]/Quantum Physics [quant-ph]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this note, we analyze joint probability distributions that come from the outcomes of quantum measurements performed on sets of quantum states. First, we identify the properties of these distributions that need to be fulfilled to recover a classical behavior. Secondly, we connect the existence of a joint distribution with the "on-state" permutability (commutativity of more than two operators) of measurement operators. By "on-state" we mean properties of operators that can hold only on a subset of states in the Hilbert space. Then, we disprove a conjecture proposed by Carstens, Ebrahimi, Tabia, and Unruh (eprint 2018), which states that partial on-state permutation imply full on-state permutation. We disprove such a conjecture with a counterexample where pairwise "on-state" commutativity does not imply on-state permutability, unlike in the case where the definition is valid for all states in the Hilbert space. Finally, we explore the new concept of on-state commutativity by showing a simple proof that if two projections almost on-state commute, then there is a commuting pair of operators that are on-state close to the originals. This result was originally proven by Hasting (Communications in Mathematical Physics, 2019) for general operators.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="regroupinstitution" xml:id="struct-120654" status="VALID">
          <idno type="IdRef">026431610</idno>
          <idno type="ISNI">0000 0000 8499 2262</idno>
          <idno type="ROR">https://ror.org/04dkp9463</idno>
          <idno type="Wikidata">Q214341</idno>
          <orgName>Universiteit van Amsterdam = University of Amsterdam</orgName>
          <orgName type="acronym">UvA</orgName>
          <date type="start">1632-01-01</date>
          <desc>
            <address>
              <addrLine>Spui 21 1012 WX Amsterdam</addrLine>
              <country key="NL"/>
            </address>
            <ref type="url">https://www.uva.nl/</ref>
          </desc>
        </org>
        <org type="researchteam" xml:id="struct-541726" status="VALID">
          <orgName>Information Quantique [LIP6]</orgName>
          <orgName type="acronym">QI</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-541703" type="direct"/>
            <relation active="#struct-413221" type="indirect"/>
            <relation name="UMR7606" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-541703" status="VALID">
          <idno type="IdRef">13558292X</idno>
          <idno type="RNSR">199712651U</idno>
          <idno type="ROR">https://ror.org/05krcen59</idno>
          <orgName>LIP6</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <addrLine>4 Place JUSSIEU 75252 PARIS CEDEX 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lip6.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413221" type="direct"/>
            <relation name="UMR7606" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-413221" status="VALID">
          <idno type="IdRef">221333754</idno>
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Sorbonne Université</orgName>
          <orgName type="acronym">SU</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <addrLine>21 rue de l’École de médecine - 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sorbonne-universite.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>