Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics
The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a coun...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1292 |
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| author | Florio M. Ciaglia Fabio Di Cosmo Alberto Ibort Giuseppe Marmo |
| author_facet | Florio M. Ciaglia Fabio Di Cosmo Alberto Ibort Giuseppe Marmo |
| author_sort | Florio M. Ciaglia |
| collection | DOAJ |
| description | The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one. |
| first_indexed | 2024-03-10T14:51:53Z |
| format | Article |
| id | doaj.art-78db50e999db408095442cd2bd693abd |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T14:51:53Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-78db50e999db408095442cd2bd693abd2023-11-20T20:55:56ZengMDPI AGEntropy1099-43002020-11-012211129210.3390/e22111292Evolution of Classical and Quantum States in the Groupoid Picture of Quantum MechanicsFlorio M. Ciaglia0Fabio Di Cosmo1Alberto Ibort2Giuseppe Marmo3Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, GermanyICMAT, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Nicolás Cabrera, 13-15, Campus de Cantoblanco, UAM, 28049 Madrid, SpainICMAT, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Nicolás Cabrera, 13-15, Campus de Cantoblanco, UAM, 28049 Madrid, SpainDipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, 80126 Napoli, ItalyThe evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.https://www.mdpi.com/1099-4300/22/11/1292quantum mechanicsentanglementSchwinger’s selective measurementscomposite systemsgroupoids picture of quantum mechanicsgroupoids |
| spellingShingle | Florio M. Ciaglia Fabio Di Cosmo Alberto Ibort Giuseppe Marmo Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics Entropy quantum mechanics entanglement Schwinger’s selective measurements composite systems groupoids picture of quantum mechanics groupoids |
| title | Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics |
| title_full | Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics |
| title_fullStr | Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics |
| title_full_unstemmed | Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics |
| title_short | Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics |
| title_sort | evolution of classical and quantum states in the groupoid picture of quantum mechanics |
| topic | quantum mechanics entanglement Schwinger’s selective measurements composite systems groupoids picture of quantum mechanics groupoids |
| url | https://www.mdpi.com/1099-4300/22/11/1292 |
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