The Operational Choi-Jamiołkowski Isomorphism

In this article, I use an operational formulation of the Choi-Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be...

Full description

Saved in:
Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2020-09, Vol.22 (9), p.1063
Main Author: Adlam, Emily
Format: Article
Language:English
Subjects:
generalized probabilistic theories
ontology
quantum foundations
quantum state
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c441t-22f6af541fcdddb4a869899070a779e08b00da7cac0766c5783e5644fb538a023
cites cdi_FETCH-LOGICAL-c441t-22f6af541fcdddb4a869899070a779e08b00da7cac0766c5783e5644fb538a023
container_end_page
container_issue 9
container_start_page 1063
container_title Entropy (Basel, Switzerland)
container_volume 22
creator Adlam, Emily
description In this article, I use an operational formulation of the Choi-Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi-Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.
doi_str_mv 10.3390/E22091063
format article
fullrecord <record><control><sourceid>proquest_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_95ff6d48c17b4a8db882bce78a2d96e6</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_95ff6d48c17b4a8db882bce78a2d96e6</doaj_id><sourcerecordid>2468336582</sourcerecordid><originalsourceid>FETCH-LOGICAL-c441t-22f6af541fcdddb4a869899070a779e08b00da7cac0766c5783e5644fb538a023</originalsourceid><addsrcrecordid>eNpVkbtOAzEQRS0E4hEo-AGUEooFv9aPBglFAYIi0UBtzdpeYtiNg70B0fJv_BcbAgiqGc1cnbmai9AhwaeMaXw2phRrggXbQLsEa11whvHmn34H7eX8iDFllIhttMMYVUIxuotO72Z-eLvwCboQ59AMR7MYihtoQ_x4f4qv-SkMJzm2MS1mIbf7aKuGJvuD7zpA95fju9F1Mb29mowupoXlnHQFpbWAuuSkts65ioMSWmmNJQYptceqwtiBtGCxFMKWUjFfCs7rqmQKepsDNFlzXYRHs0ihhfRmIgTzNYjpwUDqgm280WVdC8eVJXJ1yFVK0cp6qYA6LbzoWedr1mJZtd5ZP-8SNP-g_zfzMDMP8cXIUkvCSQ84_gak-Lz0uTNtyNY3Dcx9XGZDef9LJkq18n2yltoUc06-_j1DsFllZfxPVr326K-vX-VPOOwTkueOnA</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2468336582</pqid></control><display><type>article</type><title>The Operational Choi-Jamiołkowski Isomorphism</title><source>DOAJ Directory of Open Access Journals</source><source>Publicly Available Content (ProQuest)</source><source>PubMed Central</source><creator>Adlam, Emily</creator><creatorcontrib>Adlam, Emily</creatorcontrib><description>In this article, I use an operational formulation of the Choi-Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi-Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.</description><identifier>ISSN: 1099-4300</identifier><identifier>EISSN: 1099-4300</identifier><identifier>DOI: 10.3390/E22091063</identifier><identifier>PMID: 33286832</identifier><language>eng</language><publisher>Switzerland: MDPI</publisher><subject>generalized probabilistic theories ; ontology ; quantum foundations ; quantum state</subject><ispartof>Entropy (Basel, Switzerland), 2020-09, Vol.22 (9), p.1063</ispartof><rights>2020 by the author. 2020</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c441t-22f6af541fcdddb4a869899070a779e08b00da7cac0766c5783e5644fb538a023</citedby><cites>FETCH-LOGICAL-c441t-22f6af541fcdddb4a869899070a779e08b00da7cac0766c5783e5644fb538a023</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC7597141/pdf/$$EPDF$$P50$$Gpubmedcentral$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC7597141/$$EHTML$$P50$$Gpubmedcentral$$Hfree_for_read</linktohtml><link.rule.ids>230,314,727,780,784,864,885,2102,27924,27925,37013,53791,53793</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/33286832$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Adlam, Emily</creatorcontrib><title>The Operational Choi-Jamiołkowski Isomorphism</title><title>Entropy (Basel, Switzerland)</title><addtitle>Entropy (Basel)</addtitle><description>In this article, I use an operational formulation of the Choi-Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi-Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.</description><subject>generalized probabilistic theories</subject><subject>ontology</subject><subject>quantum foundations</subject><subject>quantum state</subject><issn>1099-4300</issn><issn>1099-4300</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>DOA</sourceid><recordid>eNpVkbtOAzEQRS0E4hEo-AGUEooFv9aPBglFAYIi0UBtzdpeYtiNg70B0fJv_BcbAgiqGc1cnbmai9AhwaeMaXw2phRrggXbQLsEa11whvHmn34H7eX8iDFllIhttMMYVUIxuotO72Z-eLvwCboQ59AMR7MYihtoQ_x4f4qv-SkMJzm2MS1mIbf7aKuGJvuD7zpA95fju9F1Mb29mowupoXlnHQFpbWAuuSkts65ioMSWmmNJQYptceqwtiBtGCxFMKWUjFfCs7rqmQKepsDNFlzXYRHs0ihhfRmIgTzNYjpwUDqgm280WVdC8eVJXJ1yFVK0cp6qYA6LbzoWedr1mJZtd5ZP-8SNP-g_zfzMDMP8cXIUkvCSQ84_gak-Lz0uTNtyNY3Dcx9XGZDef9LJkq18n2yltoUc06-_j1DsFllZfxPVr326K-vX-VPOOwTkueOnA</recordid><startdate>20200922</startdate><enddate>20200922</enddate><creator>Adlam, Emily</creator><general>MDPI</general><general>MDPI AG</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>5PM</scope><scope>DOA</scope></search><sort><creationdate>20200922</creationdate><title>The Operational Choi-Jamiołkowski Isomorphism</title><author>Adlam, Emily</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c441t-22f6af541fcdddb4a869899070a779e08b00da7cac0766c5783e5644fb538a023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>generalized probabilistic theories</topic><topic>ontology</topic><topic>quantum foundations</topic><topic>quantum state</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Adlam, Emily</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Entropy (Basel, Switzerland)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Adlam, Emily</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Operational Choi-Jamiołkowski Isomorphism</atitle><jtitle>Entropy (Basel, Switzerland)</jtitle><addtitle>Entropy (Basel)</addtitle><date>2020-09-22</date><risdate>2020</risdate><volume>22</volume><issue>9</issue><spage>1063</spage><pages>1063-</pages><issn>1099-4300</issn><eissn>1099-4300</eissn><abstract>In this article, I use an operational formulation of the Choi-Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi-Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.</abstract><cop>Switzerland</cop><pub>MDPI</pub><pmid>33286832</pmid><doi>10.3390/E22091063</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1099-4300
ispartof Entropy (Basel, Switzerland), 2020-09, Vol.22 (9), p.1063
issn 1099-4300
1099-4300
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_95ff6d48c17b4a8db882bce78a2d96e6
source DOAJ Directory of Open Access Journals; Publicly Available Content (ProQuest); PubMed Central
subjects generalized probabilistic theories
ontology
quantum foundations
quantum state
title The Operational Choi-Jamiołkowski Isomorphism
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-24T13%3A40%3A57IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Operational%20Choi-Jamio%C5%82kowski%20Isomorphism&rft.jtitle=Entropy%20(Basel,%20Switzerland)&rft.au=Adlam,%20Emily&rft.date=2020-09-22&rft.volume=22&rft.issue=9&rft.spage=1063&rft.pages=1063-&rft.issn=1099-4300&rft.eissn=1099-4300&rft_id=info:doi/10.3390/E22091063&rft_dat=%3Cproquest_doaj_%3E2468336582%3C/proquest_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c441t-22f6af541fcdddb4a869899070a779e08b00da7cac0766c5783e5644fb538a023%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2468336582&rft_id=info:pmid/33286832&rfr_iscdi=true