Decoupling with unitary approximate two-designs
Consider a bipartite system, of which one subsystem, A , undergoes a physical evolution separated from the other subsystem, R . One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R , i.e. decouples the subsystems. A quantitative answer t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2013-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/15/5/053022 |
| _version_ | 1797751614522523648 |
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| author | Oleg Szehr Frédéric Dupuis Marco Tomamichel Renato Renner |
| author_facet | Oleg Szehr Frédéric Dupuis Marco Tomamichel Renato Renner |
| author_sort | Oleg Szehr |
| collection | DOAJ |
| description | Consider a bipartite system, of which one subsystem, A , undergoes a physical evolution separated from the other subsystem, R . One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R , i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems , which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate two-designs are appropriate for decoupling even if the dimension of this system is large. |
| first_indexed | 2024-03-12T16:52:05Z |
| format | Article |
| id | doaj.art-e599e5eebdf042388eff93de624267bb |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:52:05Z |
| publishDate | 2013-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-e599e5eebdf042388eff93de624267bb2023-08-08T11:09:27ZengIOP PublishingNew Journal of Physics1367-26302013-01-0115505302210.1088/1367-2630/15/5/053022Decoupling with unitary approximate two-designsOleg Szehr0Frédéric Dupuis1Marco Tomamichel2Renato Renner3Zentrum Mathematik, Technische Universität München , D-85748 Garching, Germany; Institute for Theoretical Physics , ETH Zurich, CH-8093 Zurich, SwitzerlandInstitute for Theoretical Physics , ETH Zurich, CH-8093 Zurich, Switzerland; Department of Computer Science, Aarhus University , DK-8200 Aarhus N, DenmarkInstitute for Theoretical Physics , ETH Zurich, CH-8093 Zurich, Switzerland; Centre for Quantum Technologies, National University of Singapore , Singapore 117543, SingaporeInstitute for Theoretical Physics , ETH Zurich, CH-8093 Zurich, SwitzerlandConsider a bipartite system, of which one subsystem, A , undergoes a physical evolution separated from the other subsystem, R . One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R , i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems , which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate two-designs are appropriate for decoupling even if the dimension of this system is large.https://doi.org/10.1088/1367-2630/15/5/053022 |
| spellingShingle | Oleg Szehr Frédéric Dupuis Marco Tomamichel Renato Renner Decoupling with unitary approximate two-designs New Journal of Physics |
| title | Decoupling with unitary approximate two-designs |
| title_full | Decoupling with unitary approximate two-designs |
| title_fullStr | Decoupling with unitary approximate two-designs |
| title_full_unstemmed | Decoupling with unitary approximate two-designs |
| title_short | Decoupling with unitary approximate two-designs |
| title_sort | decoupling with unitary approximate two designs |
| url | https://doi.org/10.1088/1367-2630/15/5/053022 |
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