{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T18:15:58Z","timestamp":1769883358953,"version":"3.49.0"},"reference-count":22,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,7,7]],"date-time":"2022-07-07T00:00:00Z","timestamp":1657152000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We consider a bipartite transformation that we call self-embezzlement and use it to prove a constant gap between the capabilities of two models of quantum information: the conventional model, where bipartite systems are represented by tensor products of Hilbert spaces; and a natural model of quantum information processing for abstract states on C*-algebras, where joint systems are represented by tensor products of C*-algebras. We call this the C*-circuit model and show that it is a special case of the commuting-operator model (in that it can be translated into such a model). For the conventional model, we show that there exists a constant <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>&amp;#x03F5;<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><mml:mo>&amp;#x003E;<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math> such that self-embezzlement cannot be achieved with precision parameter less than <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>&amp;#x03F5;<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><\/mml:math> (i.e., the fidelity cannot be greater than <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>1<\/mml:mn><mml:mo>&amp;#x2212;<\/mml:mo><mml:msub><mml:mi>&amp;#x03F5;<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><\/mml:math>); whereas, in the C*-circuit model---as well as in a commuting-operator model---the precision can be <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>0<\/mml:mn><\/mml:math> (i.e., fidelity <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>1<\/mml:mn><\/mml:math>).Self-embezzlement is not a non-local game, hence our results do not impact the celebrated Connes Embedding conjecture. Instead, the significance of these results is to exhibit a reasonably natural quantum information processing problem for which there is a constant gap between the capabilities of the conventional Hilbert space model and the commuting-operator or C*-circuit model.<\/jats:p>","DOI":"10.22331\/q-2022-07-07-755","type":"journal-article","created":{"date-parts":[[2022,7,7]],"date-time":"2022-07-07T12:11:58Z","timestamp":1657195918000},"page":"755","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement"],"prefix":"10.22331","volume":"6","author":[{"given":"Richard","family":"Cleve","sequence":"first","affiliation":[{"name":"Institute for Quantum Computing and Cheriton School of Computer Science, University of Waterloo, Canada."}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7061-6861","authenticated-orcid":false,"given":"Benoit","family":"Collins","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan."}]},{"given":"Li","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute for Quantum Computing and Cheriton School of Computer Science, University of Waterloo, Canada."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2361-852X","authenticated-orcid":false,"given":"Vern","family":"Paulsen","sequence":"additional","affiliation":[{"name":"Institute for Quantum Computing and Department of Pure Mathematics, University of Waterloo, Canada."}]}],"member":"9598","published-online":{"date-parts":[[2022,7,7]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. 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