Barnum, H.; Graydon, M.A.; Wilce, A.: Composites and categories of euclidean Jordan algebras. In: Quantum 4 (2020), 359. DOI: https://doi.org/10.22331/Q-2020-11-08-359
Zusammenfassung: | |
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such models. We show that no such composite has the exceptional Jordan algebra as a direct summand, nor does any such composite exist if one factor has an exceptional summand, unless the other factor is a direct sum of one-dimensional Jordan algebras (representing essentially a classical system). Moreover, we show that any composite of simple, non-exceptional EJAs is a direct summand of their universal tensor product, sharply limiting the possibilities. These results warrant our focussing on concrete Jordan algebras of hermitian matrices, i.e., euclidean Jordan algebras with a preferred embedding in a complex matrix algebra. We show that these can be organized in a natural way as a symmetric monoidal category, albeit one that is not compact closed. We then construct a related category InvQM of embedded euclidean Jordan algebras, having fewer objects but more morphisms, that is not only compact closed but dagger-compact. This category unifies finite-dimensional real, complex and quaternionic mixed-state quantum mechanics, except that the composite of two complex quantum systems comes with an extra classical bit. Our notion of composite requires neither tomographic locality, nor preservation of purity under tensor product. The categories we construct include examples in which both of these conditions fail. In such cases, the information capacity (the maximum number of mutually distinguishable states) of a composite is greater than the product of the capacities of its constituents. © 2020 FahrenHouse. All rights reserved. | |
Lizenzbestimmungen: | CC BY 4.0 Unported |
Publikationstyp: | Article |
Publikationsstatus: | publishedVersion |
Erstveröffentlichung: | 2020 |
Die Publikation erscheint in Sammlung(en): | Forschungsinitiativen |
Pos. | Land | Downloads | ||
---|---|---|---|---|
Anzahl | Proz. | |||
1 | United States | 45 | 33,09% | |
2 | Germany | 39 | 28,68% | |
3 | No geo information available | 7 | 5,15% | |
4 | China | 7 | 5,15% | |
5 | Indonesia | 5 | 3,68% | |
6 | France | 3 | 2,21% | |
7 | Netherlands | 2 | 1,47% | |
8 | Iran, Islamic Republic of | 2 | 1,47% | |
9 | United Kingdom | 2 | 1,47% | |
10 | Europe | 2 | 1,47% | |
andere | 22 | 16,18% |
Hinweis
Zur Erhebung der Downloadstatistiken kommen entsprechend dem „COUNTER Code of Practice for e-Resources“ international anerkannte Regeln und Normen zur Anwendung. COUNTER ist eine internationale Non-Profit-Organisation, in der Bibliotheksverbände, Datenbankanbieter und Verlage gemeinsam an Standards zur Erhebung, Speicherung und Verarbeitung von Nutzungsdaten elektronischer Ressourcen arbeiten, welche so Objektivität und Vergleichbarkeit gewährleisten sollen. Es werden hierbei ausschließlich Zugriffe auf die entsprechenden Volltexte ausgewertet, keine Aufrufe der Website an sich.