Device-independent test of causal order and relations to fixed-points
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, imp...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2016-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/18/3/035014 |
| _version_ | 1797751035135000576 |
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| author | Ämin Baumeler Stefan Wolf |
| author_facet | Ämin Baumeler Stefan Wolf |
| author_sort | Ämin Baumeler |
| collection | DOAJ |
| description | Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities—just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical consistency allows for violating causal inequalities. Here, we show that a classical environment (with which the parties interact), possibly containing loops, is logically consistent if and only if whatever the involved parties do, there is exactly one fixed-point, the latter being representable as a mixture of deterministic fixed-points. We further show that the non-causal view allows for a model of computation strictly more powerful than computation in a world of fixed causal orders. |
| first_indexed | 2024-03-12T16:41:30Z |
| format | Article |
| id | doaj.art-7b33fda2e3cb4f49b2afa86caff2b445 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:41:30Z |
| publishDate | 2016-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-7b33fda2e3cb4f49b2afa86caff2b4452023-08-08T14:27:39ZengIOP PublishingNew Journal of Physics1367-26302016-01-0118303501410.1088/1367-2630/18/3/035014Device-independent test of causal order and relations to fixed-pointsÄmin Baumeler0Stefan Wolf1Faculty of Informatics, Universitá della Svizzera italiana , Via G. Buffi 13, 6900 Lugano, Switzerland; Facoltà indipendente di Gandria, Lunga scala, 6978 Gandria, SwitzerlandFaculty of Informatics, Universitá della Svizzera italiana , Via G. Buffi 13, 6900 Lugano, Switzerland; Facoltà indipendente di Gandria, Lunga scala, 6978 Gandria, SwitzerlandBell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities—just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical consistency allows for violating causal inequalities. Here, we show that a classical environment (with which the parties interact), possibly containing loops, is logically consistent if and only if whatever the involved parties do, there is exactly one fixed-point, the latter being representable as a mixture of deterministic fixed-points. We further show that the non-causal view allows for a model of computation strictly more powerful than computation in a world of fixed causal orders.https://doi.org/10.1088/1367-2630/18/3/035014device-independentcausal orderfixed-pointscomputationnon-causal |
| spellingShingle | Ämin Baumeler Stefan Wolf Device-independent test of causal order and relations to fixed-points New Journal of Physics device-independent causal order fixed-points computation non-causal |
| title | Device-independent test of causal order and relations to fixed-points |
| title_full | Device-independent test of causal order and relations to fixed-points |
| title_fullStr | Device-independent test of causal order and relations to fixed-points |
| title_full_unstemmed | Device-independent test of causal order and relations to fixed-points |
| title_short | Device-independent test of causal order and relations to fixed-points |
| title_sort | device independent test of causal order and relations to fixed points |
| topic | device-independent causal order fixed-points computation non-causal |
| url | https://doi.org/10.1088/1367-2630/18/3/035014 |
| work_keys_str_mv | AT aminbaumeler deviceindependenttestofcausalorderandrelationstofixedpoints AT stefanwolf deviceindependenttestofcausalorderandrelationstofixedpoints |