<?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-05333097</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="2026-04-27T17:24:03+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources and Detectors</title>
            <author role="aut">
              <persName>
                <forename type="first">Nicolas</forename>
                <surname>Heurtel</surname>
              </persName>
              <email type="md5">949ee07cc8be9e57c886296d751ad2d0</email>
              <email type="domain">quandela.com</email>
              <idno type="idhal" notation="string">nicolas-heurtel</idno>
              <idno type="idhal" notation="numeric">1334203</idno>
              <idno type="halauthorid" notation="string">2659914-1334203</idno>
              <affiliation ref="#struct-1057527"/>
              <affiliation ref="#struct-1086683"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Nicolas</forename>
                <surname>Heurtel</surname>
              </persName>
              <email type="md5">949ee07cc8be9e57c886296d751ad2d0</email>
              <email type="domain">quandela.com</email>
            </editor>
            <funder ref="#projanr-75279"/>
            <funder ref="#projanr-57829"/>
            <funder ref="#projanr-98195"/>
            <funder ref="#projanr-98217"/>
            <funder ref="#projanr-77965"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-10-27 11:30:57</date>
              <date type="whenModified">2026-02-25 16:18:02</date>
              <date type="whenReleased">2025-10-27 14:13:44</date>
              <date type="whenProduced">2025-02-10</date>
              <date type="whenEndEmbargoed">2025-10-27</date>
              <ref type="file" target="https://hal.science/hal-05333097v1/document">
                <date notBefore="2025-10-27"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-05333097v1/file/2402.17693v2.pdf" id="file-5333097-4566441">
                <date notBefore="2025-10-27"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2402.17693"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1324883">
                <persName>
                  <forename>Nicolas</forename>
                  <surname>Heurtel</surname>
                </persName>
                <email type="md5">949ee07cc8be9e57c886296d751ad2d0</email>
                <email type="domain">quandela.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-05333097</idno>
            <idno type="halUri">https://hal.science/hal-05333097</idno>
            <idno type="halBibtex">heurtel:hal-05333097</idno>
            <idno type="halRefHtml">&lt;i&gt;CSL 2025 - 33rd EACSL Annual Conference on Computer Science Logic&lt;/i&gt;, Feb 2025, Amsterdam, Netherlands. &lt;a target="_blank" href="https://dx.doi.org/10.4230/LIPIcs.CSL.2025.38"&gt;&amp;#x27E8;10.4230/LIPIcs.CSL.2025.38&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">CSL 2025 - 33rd EACSL Annual Conference on Computer Science Logic, Feb 2025, Amsterdam, Netherlands. &amp;#x27E8;10.4230/LIPIcs.CSL.2025.38&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0 - Attribution<ref corresp="#file-5333097-4566441"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="ENS-CACHAN">Ecole Normale Supérieure de Cachan</idno>
            <idno type="stamp" n="INRIA-SACLAY" corresp="INRIA">INRIA Saclay - Ile de France</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="CENTRALESUPELEC">Ecole CentraleSupélec</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIVERSITE-PARIS-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="ENS-PARIS-SACLAY">Ecole Normale Supérieure paris-Saclay</idno>
            <idno type="stamp" n="ENS-PSACLAY">Ecole Normale Supérieure Paris-Saclay</idno>
            <idno type="stamp" n="GS-COMPUTER-SCIENCE">Graduate School Computer Science</idno>
            <idno type="stamp" n="LMF">Laboratoire Méthodes Formelles</idno>
            <idno type="stamp" n="LMF-QUANT">Informatique Quantique</idno>
            <idno type="stamp" n="PEPR_QUANTIQUE">PEPR Quantique</idno>
            <idno type="stamp" n="ANR_QUANTIQUE">ANR QUANTIQUE</idno>
            <idno type="stamp" n="ANR_QUANTIQUE_1" corresp="ANR_QUANTIQUE">ANR_QUANTIQUE_1</idno>
            <idno type="stamp" n="ANR_QUANTIQUE_3" corresp="ANR_QUANTIQUE">ANR_QUANTIQUE_3</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="0">No</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources and Detectors</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Nicolas</forename>
                    <surname>Heurtel</surname>
                  </persName>
                  <email type="md5">949ee07cc8be9e57c886296d751ad2d0</email>
                  <email type="domain">quandela.com</email>
                  <idno type="idhal" notation="string">nicolas-heurtel</idno>
                  <idno type="idhal" notation="numeric">1334203</idno>
                  <idno type="halauthorid" notation="string">2659914-1334203</idno>
                  <affiliation ref="#struct-1057527"/>
                  <affiliation ref="#struct-1086683"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>CSL 2025 - 33rd EACSL Annual Conference on Computer Science Logic</title>
                  <date type="start">2025-02-10</date>
                  <date type="end">2025-02-14</date>
                  <settlement>Amsterdam</settlement>
                  <country key="NL">Netherlands</country>
                </meeting>
                <imprint>
                  <publisher>Schloss Dagstuhl – Leibniz-Zentrum für Informatik</publisher>
                  <date type="datePub">2025</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2402.17693</idno>
              <idno type="doi">10.4230/LIPIcs.CSL.2025.38</idno>
              <ref type="publisher">https://csl2025.github.io/</ref>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Fock Space</term>
                <term xml:lang="en">Completeness</term>
                <term xml:lang="en">Linear Optical Quantum Computing</term>
                <term xml:lang="en">Linear Optical Circuits</term>
                <term xml:lang="en">Graphical Language</term>
                <term xml:lang="en">Quantum Computing</term>
              </keywords>
              <classCode scheme="https://dl.acm.org/ccs" n="ACM2012.F"/>
              <classCode scheme="https://dl.acm.org/ccs" n="ACM2012.F.1.2"/>
              <classCode scheme="halDomain" n="info.info-lo">Computer Science [cs]/Logic in Computer Science [cs.LO]</classCode>
              <classCode scheme="halDomain" n="phys.qphy">Physics [physics]/Quantum Physics [quant-ph]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Graphical languages are powerful and useful to represent, rewrite and simplify different kinds of processes. In particular, they have been widely used for quantum processes, improving the state of the art for compilation, simulation and verification. In this work, we focus on one of the main carrier of quantum information and computation: linear optical circuits. We introduce the LO f i -calculus, the first graphical language to reason on the infinite-dimensional photonic space with circuits only composed of the four core elements of linear optics: the phase shifter, the beam splitter, and auxiliary sources and detectors with bounded photon number. First, we study the subfragment of circuits composed of phase shifters and beam splitters, for which we provide the first minimal equational theory. Next, we introduce a rewriting procedure on those LO f i -circuits that converge to normal forms. We prove those forms to be unique, establishing both a novel and unique representation of linear optical processes. Finally, we complement the language with an equational theory that we prove to be complete: two LO f i -circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LO f i -calculus.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-1057527" status="VALID">
          <orgName>Quandela SAS</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.quandela.com/</ref>
          </desc>
        </org>
        <org type="researchteam" xml:id="struct-1086683" status="VALID">
          <idno type="RNSR">202124178U</idno>
          <idno type="ROR">https://ror.org/042s1r231</idno>
          <orgName>Quantum Computation Structures</orgName>
          <orgName type="acronym">QuaCS</orgName>
          <date type="start">2021-12-01</date>
          <date type="end">2026-07-31</date>
          <desc>
            <address>
              <addrLine>ENS Paris Saclay, 4, avenue des Sciences, 91190Gif-sur-Yvette, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.inria.fr/fr/quacs</ref>
          </desc>
          <listRelation>
            <relation active="#struct-1065710" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-411575" type="indirect"/>
            <relation active="#struct-419361" type="indirect"/>
            <relation name="UMR9021" active="#struct-441569" type="indirect"/>
            <relation active="#struct-523723" type="indirect"/>
            <relation active="#struct-1225627" type="direct"/>
            <relation active="#struct-118511" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1065710" status="VALID">
          <idno type="IdRef">25474589X</idno>
          <idno type="RNSR">202123712M</idno>
          <idno type="ROR">https://ror.org/00gdtta79</idno>
          <idno type="Wikidata">Q109042513</idno>
          <orgName>Laboratoire Méthodes Formelles</orgName>
          <orgName type="acronym">LMF</orgName>
          <date type="start">2021-01-01</date>
          <desc>
            <address>
              <addrLine>4, avenue des Sciences, 91190, Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-411575" type="direct"/>
            <relation active="#struct-419361" type="direct"/>
            <relation name="UMR9021" active="#struct-441569" type="direct"/>
            <relation active="#struct-523723" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-411575" status="VALID">
          <idno type="IdRef">184443237</idno>
          <idno type="ROR">https://ror.org/019tcpt25</idno>
          <orgName>CentraleSupélec</orgName>
          <desc>
            <address>
              <addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.centralesupelec.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-419361" status="VALID">
          <idno type="IdRef">241345251</idno>
          <idno type="ROR">https://ror.org/03xjwb503</idno>
          <orgName>Université Paris-Saclay</orgName>
          <desc>
            <address>
              <addrLine>Bâtiment Bréguet, 3 Rue Joliot Curie 2e ét, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-paris-saclay.fr/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>
        <org type="institution" xml:id="struct-523723" status="VALID">
          <idno type="ROR">https://ror.org/00hx6zz33</idno>
          <orgName>Ecole Normale Supérieure  Paris-Saclay</orgName>
          <orgName type="acronym">ENS Paris Saclay</orgName>
          <desc>
            <address>
              <addrLine>4 avenue des Sciences, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://ens-paris-saclay.fr/</ref>
          </desc>
        </org>
        <org type="department" xml:id="struct-1225627" status="VALID">
          <idno type="ROR">https://ror.org/040753f36</idno>
          <orgName>Centre Inria de l'Université Paris-Saclay</orgName>
          <date type="start">2022-11-01</date>
          <desc>
            <address>
              <addrLine>9 Rue Joliot Curie, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-118511" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-118511" status="VALID">
          <idno type="RNSR">200818248E</idno>
          <idno type="ROR">https://ror.org/0315e5x55</idno>
          <orgName>Centre Inria de Saclay</orgName>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/saclay</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-75279" status="VALID">
          <idno type="anr">ANR-22-CE47-0012</idno>
          <orgName>TaQC</orgName>
          <desc>Dompter la causalité quantique</desc>
          <date type="start">2022</date>
        </org>
        <org type="anrProject" xml:id="projanr-57829" status="VALID">
          <idno type="anr">ANR-22-PETQ-0007</idno>
          <orgName>EPiQ</orgName>
          <desc>Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l'informatique quantique</desc>
          <date type="start">2022</date>
        </org>
        <org type="anrProject" xml:id="projanr-98195" status="VALID">
          <idno type="anr">ANR-22-PNCQ-0001</idno>
          <orgName>HQI – Acquisition</orgName>
          <desc>Initiative Nationale Hybride HPC Quantique - Acquisition</desc>
          <date type="start">2022</date>
        </org>
        <org type="anrProject" xml:id="projanr-98217" status="VALID">
          <idno type="anr">ANR-22-PETQ-0013</idno>
          <orgName>OQULUS</orgName>
          <desc>Ordinateurs quantiques à base de lumière en variables discrètes et continues</desc>
          <date type="start">2022</date>
        </org>
        <org type="anrProject" xml:id="projanr-77965" status="VALID">
          <idno type="anr">ANR-22-PNCQ-0002</idno>
          <orgName>HQI – R&amp;amp;D et Support</orgName>
          <desc>Initiative Nationale Hybride HPC Quantique – R&amp;D et Support des communautés</desc>
          <date type="start">2022</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>