Thermodynamics and the structure of quantum theory
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by study...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
19 April 2017
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| In: |
New journal of physics
Year: 2017, Volume: 19, Issue: 4 |
| ISSN: | 1367-2630 |
| DOI: | 10.1088/1367-2630/aa68ef |
| Online Access: | Verlag, kostenfrei, Volltext: http://dx.doi.org/10.1088/1367-2630/aa68ef Verlag, kostenfrei, Volltext: http://stacks.iop.org/1367-2630/19/i=4/a=043025 
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| Author Notes: | Marius Krumm, Howard Barnum, Jonathan Barrett and Markus P. Müller |
| Summary: | Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behaviour should arguably satisfy. In the framework of generalised probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin’s notion of higher-order interference. |
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| Item Description: | Gesehen am 16.10.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1367-2630 |
| DOI: | 10.1088/1367-2630/aa68ef |