Connectivity for quantum graphs
In Quantum Information Theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper a definition of connectedness for quantum graphs is provided,...
Gespeichert in:
| Veröffentlicht in: | Linear algebra and its applications 2021-01, Vol.608, p.37-53 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 53 |
|---|---|
| container_issue | |
| container_start_page | 37 |
| container_title | Linear algebra and its applications |
| container_volume | 608 |
| creator | Chávez-Domínguez, Javier Alejandro Swift, Andrew T. |
| description | In Quantum Information Theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper a definition of connectedness for quantum graphs is provided, which generalizes the classical definition. It is shown that several examples of well-known quantum graphs (quantum Hamming cubes and quantum expanders) are connected. A quantum version of a particular case of the classical tree-packing theorem from Graph Theory is also proved. Generalizations for the related notions of k-connectedness and of orthogonal representation are also proposed for quantum graphs, and it is shown that orthogonal representations have the same implications for connectedness as they do in the classical case. |
| doi_str_mv | 10.1016/j.laa.2020.08.020 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2486190664</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0024379520303931</els_id><sourcerecordid>2486190664</sourcerecordid><originalsourceid>FETCH-LOGICAL-c368t-8d70d8f18f2b9a2e92ae2118a23ff3d1fa36d0739566d271a1e605d025adbe163</originalsourceid><addsrcrecordid>eNp9kE1LxDAURYMoWEd_gCsLrlvfS9o0xZUUv2DAja5Dpkk0ZabtJO3A_Hsz1LWrs7nnfVxCbhFyBOQPXb5VKqdAIQeRR5yRBEXFMhQlPycJAC0yVtXlJbkKoQOAogKakLtm6HvTTu7gpmNqB5_uZ9VP8y799mr8CdfkwqptMDd_XJGvl-fP5i1bf7y-N0_rrGVcTJnQFWhhUVi6qRU1NVWGIgpFmbVMo1WMa6hYXXKuaYUKDYdSAy2V3hjkbEXul7mjH_azCZPshtn3caWkheBYA-dFTOGSav0QgjdWjt7tlD9KBHnqQXYy9iBPPUgQMiI6j4tj4vkHZ7wMrTN9a7Tz8XGpB_eP_QulbWOb</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2486190664</pqid></control><display><type>article</type><title>Connectivity for quantum graphs</title><source>Access via ScienceDirect (Elsevier)</source><creator>Chávez-Domínguez, Javier Alejandro ; Swift, Andrew T.</creator><creatorcontrib>Chávez-Domínguez, Javier Alejandro ; Swift, Andrew T.</creatorcontrib><description>In Quantum Information Theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper a definition of connectedness for quantum graphs is provided, which generalizes the classical definition. It is shown that several examples of well-known quantum graphs (quantum Hamming cubes and quantum expanders) are connected. A quantum version of a particular case of the classical tree-packing theorem from Graph Theory is also proved. Generalizations for the related notions of k-connectedness and of orthogonal representation are also proposed for quantum graphs, and it is shown that orthogonal representations have the same implications for connectedness as they do in the classical case.</description><identifier>ISSN: 0024-3795</identifier><identifier>EISSN: 1873-1856</identifier><identifier>DOI: 10.1016/j.laa.2020.08.020</identifier><language>eng</language><publisher>Amsterdam: Elsevier Inc</publisher><subject>Channels ; Cubes ; Expanders ; Graph theory ; Graphs ; Information theory ; Linear algebra ; Non-commutative graphs ; Operator systems ; Orthogonal representations ; Quantum expanders ; Quantum graphs ; Quantum phenomena ; Representations</subject><ispartof>Linear algebra and its applications, 2021-01, Vol.608, p.37-53</ispartof><rights>2020 Elsevier Inc.</rights><rights>Copyright American Elsevier Company, Inc. Jan 1, 2021</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c368t-8d70d8f18f2b9a2e92ae2118a23ff3d1fa36d0739566d271a1e605d025adbe163</citedby><cites>FETCH-LOGICAL-c368t-8d70d8f18f2b9a2e92ae2118a23ff3d1fa36d0739566d271a1e605d025adbe163</cites><orcidid>0000-0001-5061-3612</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.laa.2020.08.020$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Chávez-Domínguez, Javier Alejandro</creatorcontrib><creatorcontrib>Swift, Andrew T.</creatorcontrib><title>Connectivity for quantum graphs</title><title>Linear algebra and its applications</title><description>In Quantum Information Theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper a definition of connectedness for quantum graphs is provided, which generalizes the classical definition. It is shown that several examples of well-known quantum graphs (quantum Hamming cubes and quantum expanders) are connected. A quantum version of a particular case of the classical tree-packing theorem from Graph Theory is also proved. Generalizations for the related notions of k-connectedness and of orthogonal representation are also proposed for quantum graphs, and it is shown that orthogonal representations have the same implications for connectedness as they do in the classical case.</description><subject>Channels</subject><subject>Cubes</subject><subject>Expanders</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Information theory</subject><subject>Linear algebra</subject><subject>Non-commutative graphs</subject><subject>Operator systems</subject><subject>Orthogonal representations</subject><subject>Quantum expanders</subject><subject>Quantum graphs</subject><subject>Quantum phenomena</subject><subject>Representations</subject><issn>0024-3795</issn><issn>1873-1856</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAURYMoWEd_gCsLrlvfS9o0xZUUv2DAja5Dpkk0ZabtJO3A_Hsz1LWrs7nnfVxCbhFyBOQPXb5VKqdAIQeRR5yRBEXFMhQlPycJAC0yVtXlJbkKoQOAogKakLtm6HvTTu7gpmNqB5_uZ9VP8y799mr8CdfkwqptMDd_XJGvl-fP5i1bf7y-N0_rrGVcTJnQFWhhUVi6qRU1NVWGIgpFmbVMo1WMa6hYXXKuaYUKDYdSAy2V3hjkbEXul7mjH_azCZPshtn3caWkheBYA-dFTOGSav0QgjdWjt7tlD9KBHnqQXYy9iBPPUgQMiI6j4tj4vkHZ7wMrTN9a7Tz8XGpB_eP_QulbWOb</recordid><startdate>20210101</startdate><enddate>20210101</enddate><creator>Chávez-Domínguez, Javier Alejandro</creator><creator>Swift, Andrew T.</creator><general>Elsevier Inc</general><general>American Elsevier Company, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-5061-3612</orcidid></search><sort><creationdate>20210101</creationdate><title>Connectivity for quantum graphs</title><author>Chávez-Domínguez, Javier Alejandro ; Swift, Andrew T.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-8d70d8f18f2b9a2e92ae2118a23ff3d1fa36d0739566d271a1e605d025adbe163</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Channels</topic><topic>Cubes</topic><topic>Expanders</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Information theory</topic><topic>Linear algebra</topic><topic>Non-commutative graphs</topic><topic>Operator systems</topic><topic>Orthogonal representations</topic><topic>Quantum expanders</topic><topic>Quantum graphs</topic><topic>Quantum phenomena</topic><topic>Representations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chávez-Domínguez, Javier Alejandro</creatorcontrib><creatorcontrib>Swift, Andrew T.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Linear algebra and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chávez-Domínguez, Javier Alejandro</au><au>Swift, Andrew T.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Connectivity for quantum graphs</atitle><jtitle>Linear algebra and its applications</jtitle><date>2021-01-01</date><risdate>2021</risdate><volume>608</volume><spage>37</spage><epage>53</epage><pages>37-53</pages><issn>0024-3795</issn><eissn>1873-1856</eissn><abstract>In Quantum Information Theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper a definition of connectedness for quantum graphs is provided, which generalizes the classical definition. It is shown that several examples of well-known quantum graphs (quantum Hamming cubes and quantum expanders) are connected. A quantum version of a particular case of the classical tree-packing theorem from Graph Theory is also proved. Generalizations for the related notions of k-connectedness and of orthogonal representation are also proposed for quantum graphs, and it is shown that orthogonal representations have the same implications for connectedness as they do in the classical case.</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1016/j.laa.2020.08.020</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0001-5061-3612</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0024-3795 |
| ispartof | Linear algebra and its applications, 2021-01, Vol.608, p.37-53 |
| issn | 0024-3795 1873-1856 |
| language | eng |
| recordid | cdi_proquest_journals_2486190664 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Channels Cubes Expanders Graph theory Graphs Information theory Linear algebra Non-commutative graphs Operator systems Orthogonal representations Quantum expanders Quantum graphs Quantum phenomena Representations |
| title | Connectivity for quantum graphs |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T09%3A40%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Connectivity%20for%20quantum%20graphs&rft.jtitle=Linear%20algebra%20and%20its%20applications&rft.au=Ch%C3%A1vez-Dom%C3%ADnguez,%20Javier%20Alejandro&rft.date=2021-01-01&rft.volume=608&rft.spage=37&rft.epage=53&rft.pages=37-53&rft.issn=0024-3795&rft.eissn=1873-1856&rft_id=info:doi/10.1016/j.laa.2020.08.020&rft_dat=%3Cproquest_cross%3E2486190664%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2486190664&rft_id=info:pmid/&rft_els_id=S0024379520303931&rfr_iscdi=true |