Quantum de Finetti Theorems Under Local Measurements with Applications
Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti theorems, both showing that under tests formed by local measurements in each of the subsystems one can get an exponential improvement in the er...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2017
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| Online Access: | http://hdl.handle.net/1721.1/109902 https://orcid.org/0000-0003-3220-7682 |
| _version_ | 1826199668106723328 |
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| author | Brandão, Fernando G. S. L. Harrow, Aram W |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Brandão, Fernando G. S. L. Harrow, Aram W |
| author_sort | Brandão, Fernando G. S. L. |
| collection | MIT |
| description | Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti theorems, both showing that under tests formed by local measurements in each of the subsystems one can get an exponential improvement in the error dependence on the dimension of the subsystems. We also obtain similar results for non-signaling probability distributions. We give several applications of the results to quantum complexity theory, polynomial optimization, and quantum information theory. The proofs of the new quantum de Finetti theorems are based on information theory, in particular on the chain rule of mutual information. The results constitute improvements and generalizations of a recent de Finetti theorem due to Brandão, Christandl and Yard. |
| first_indexed | 2024-09-23T11:23:56Z |
| format | Article |
| id | mit-1721.1/109902 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:23:56Z |
| publishDate | 2017 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1099022022-09-27T19:16:59Z Quantum de Finetti Theorems Under Local Measurements with Applications Brandão, Fernando G. S. L. Harrow, Aram W Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Physics Harrow, Aram W Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti theorems, both showing that under tests formed by local measurements in each of the subsystems one can get an exponential improvement in the error dependence on the dimension of the subsystems. We also obtain similar results for non-signaling probability distributions. We give several applications of the results to quantum complexity theory, polynomial optimization, and quantum information theory. The proofs of the new quantum de Finetti theorems are based on information theory, in particular on the chain rule of mutual information. The results constitute improvements and generalizations of a recent de Finetti theorem due to Brandão, Christandl and Yard. 2017-06-15T18:26:46Z 2018-02-04T06:00:05Z 2017-04 2017-05-13T05:50:16Z Article http://purl.org/eprint/type/JournalArticle 0010-3616 1432-0916 http://hdl.handle.net/1721.1/109902 Brandão, Fernando G. S. L., and Aram W. Harrow. “Quantum de Finetti Theorems Under Local Measurements with Applications.” Communications in Mathematical Physics 353.2 (2017): 469–506. https://orcid.org/0000-0003-3220-7682 en http://dx.doi.org/10.1007/s00220-017-2880-3 Communications in Mathematical Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Brandão, Fernando G. S. L. Harrow, Aram W Quantum de Finetti Theorems Under Local Measurements with Applications |
| title | Quantum de Finetti Theorems Under Local Measurements with Applications |
| title_full | Quantum de Finetti Theorems Under Local Measurements with Applications |
| title_fullStr | Quantum de Finetti Theorems Under Local Measurements with Applications |
| title_full_unstemmed | Quantum de Finetti Theorems Under Local Measurements with Applications |
| title_short | Quantum de Finetti Theorems Under Local Measurements with Applications |
| title_sort | quantum de finetti theorems under local measurements with applications |
| url | http://hdl.handle.net/1721.1/109902 https://orcid.org/0000-0003-3220-7682 |
| work_keys_str_mv | AT brandaofernandogsl quantumdefinettitheoremsunderlocalmeasurementswithapplications AT harrowaramw quantumdefinettitheoremsunderlocalmeasurementswithapplications |