Dimension of physical systems, information processing, and thermodynamics
We ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model-independent definitions of the dimension of physical systems, based on measurements and the capacity of storing information. While both definitions are equivale...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/16/12/123050 |
| _version_ | 1827874194362204160 |
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| author | Nicolas Brunner Marc Kaplan Anthony Leverrier Paul Skrzypczyk |
| author_facet | Nicolas Brunner Marc Kaplan Anthony Leverrier Paul Skrzypczyk |
| author_sort | Nicolas Brunner |
| collection | DOAJ |
| description | We ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model-independent definitions of the dimension of physical systems, based on measurements and the capacity of storing information. While both definitions are equivalent in classical and quantum mechanics, they are different in generalized probabilistic theories. We discuss in detail the case of a theory known as ‘boxworld’, and show that such a theory features systems with dimension mismatch. This dimension mismatch can be made arbitrarily large using an amplification procedure. Furthermore, we show that the dimension mismatch of boxworld has strong consequences on its power for performing information-theoretic tasks, leading to the collapse of communication complexity and to the violation of information causality. Finally, we discuss the consequences of a dimension mismatch from the perspective of thermodynamics, and ask whether this effect could break Landauerʼs erasure principle and thus the second law. |
| first_indexed | 2024-03-12T16:48:46Z |
| format | Article |
| id | doaj.art-8fc1799994e14b209325325a381df25a |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:48:46Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-8fc1799994e14b209325325a381df25a2023-08-08T11:26:08ZengIOP PublishingNew Journal of Physics1367-26302014-01-01161212305010.1088/1367-2630/16/12/123050Dimension of physical systems, information processing, and thermodynamicsNicolas Brunner0Marc Kaplan1Anthony Leverrier2Paul Skrzypczyk3Département de Physique Théorique, Université de Genève , 1211 Genève, SwitzerlandLTCI, Télécom ParisTech, 23 avenue d’Italie, 75214 Paris CEDEX 13, FranceInria, EPI SECRET, B.P. 105, 78153 Le Chesnay Cedex, FranceICFO-Institut de Ciencies Fotoniques , Mediterranean Technology Park, 08860 Castelldefels, Barcelona, SpainWe ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model-independent definitions of the dimension of physical systems, based on measurements and the capacity of storing information. While both definitions are equivalent in classical and quantum mechanics, they are different in generalized probabilistic theories. We discuss in detail the case of a theory known as ‘boxworld’, and show that such a theory features systems with dimension mismatch. This dimension mismatch can be made arbitrarily large using an amplification procedure. Furthermore, we show that the dimension mismatch of boxworld has strong consequences on its power for performing information-theoretic tasks, leading to the collapse of communication complexity and to the violation of information causality. Finally, we discuss the consequences of a dimension mismatch from the perspective of thermodynamics, and ask whether this effect could break Landauerʼs erasure principle and thus the second law.https://doi.org/10.1088/1367-2630/16/12/123050foundations of quantum theorygeneralized theoriesinformation processing |
| spellingShingle | Nicolas Brunner Marc Kaplan Anthony Leverrier Paul Skrzypczyk Dimension of physical systems, information processing, and thermodynamics New Journal of Physics foundations of quantum theory generalized theories information processing |
| title | Dimension of physical systems, information processing, and thermodynamics |
| title_full | Dimension of physical systems, information processing, and thermodynamics |
| title_fullStr | Dimension of physical systems, information processing, and thermodynamics |
| title_full_unstemmed | Dimension of physical systems, information processing, and thermodynamics |
| title_short | Dimension of physical systems, information processing, and thermodynamics |
| title_sort | dimension of physical systems information processing and thermodynamics |
| topic | foundations of quantum theory generalized theories information processing |
| url | https://doi.org/10.1088/1367-2630/16/12/123050 |
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