Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamics
Consider an open quantum system S , interacting with its environment E. Whether the reduced dynamics of the system can be given by a linear map, or not, is an important subject, in the theory of open quantum systems. Dominy, Shabani and Lidar have proposed a general framework for linear Hermitian re...
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| Format: | Article |
| Language: | English |
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Isfahan University of Technology
2021-11-01
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| Series: | Iranian Journal of Physics Research |
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| Online Access: | http://ijpr.iut.ac.ir/article_1722_dd6b3ef3a8bf922334e6cc16fcb2a80a.pdf |
| _version_ | 1811344156866379776 |
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| author | I Sargolzahi |
| author_facet | I Sargolzahi |
| author_sort | I Sargolzahi |
| collection | DOAJ |
| description | Consider an open quantum system S , interacting with its environment E. Whether the reduced dynamics of the system can be given by a linear map, or not, is an important subject, in the theory of open quantum systems. Dominy, Shabani and Lidar have proposed a general framework for linear Hermitian reduced dynamics. They have considered the case that both the system and the environment are finite dimensional. Their framework can be generalized to include the case that the environment is infinite dimensional too. In this paper, after demonstrating this generalization, we discuss the role of the convexity of the set, of possible initial states of the system-environment, in their framework. Next, we give a proof for the existence of the operator sum representation, for arbitrary linear Hermitian map. This proof enables us to prove the Choi-Jamiołkowski and the Jamiołkowski isomorphisms, straightforwardly. |
| first_indexed | 2024-04-13T19:42:46Z |
| format | Article |
| id | doaj.art-f7f3afadc2c34a1faead5ce6ce14d2f5 |
| institution | Directory Open Access Journal |
| issn | 1682-6957 2345-3664 |
| language | English |
| last_indexed | 2024-04-13T19:42:46Z |
| publishDate | 2021-11-01 |
| publisher | Isfahan University of Technology |
| record_format | Article |
| series | Iranian Journal of Physics Research |
| spelling | doaj.art-f7f3afadc2c34a1faead5ce6ce14d2f52022-12-22T02:32:50ZengIsfahan University of TechnologyIranian Journal of Physics Research1682-69572345-36642021-11-012134514591722Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamicsI Sargolzahi0Department of Physics, University of Neyshabur, Neyshabur, IranConsider an open quantum system S , interacting with its environment E. Whether the reduced dynamics of the system can be given by a linear map, or not, is an important subject, in the theory of open quantum systems. Dominy, Shabani and Lidar have proposed a general framework for linear Hermitian reduced dynamics. They have considered the case that both the system and the environment are finite dimensional. Their framework can be generalized to include the case that the environment is infinite dimensional too. In this paper, after demonstrating this generalization, we discuss the role of the convexity of the set, of possible initial states of the system-environment, in their framework. Next, we give a proof for the existence of the operator sum representation, for arbitrary linear Hermitian map. This proof enables us to prove the Choi-Jamiołkowski and the Jamiołkowski isomorphisms, straightforwardly.http://ijpr.iut.ac.ir/article_1722_dd6b3ef3a8bf922334e6cc16fcb2a80a.pdfopen quantum systemshermitian mapscompletely positive mapsassignment mapchoi-jamiołkowski isomorphism |
| spellingShingle | I Sargolzahi Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamics Iranian Journal of Physics Research open quantum systems hermitian maps completely positive maps assignment map choi-jamiołkowski isomorphism |
| title | Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamics |
| title_full | Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamics |
| title_fullStr | Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamics |
| title_full_unstemmed | Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamics |
| title_short | Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamics |
| title_sort | generalizing the framework of dominy shabani lidar for the reduced dynamics |
| topic | open quantum systems hermitian maps completely positive maps assignment map choi-jamiołkowski isomorphism |
| url | http://ijpr.iut.ac.ir/article_1722_dd6b3ef3a8bf922334e6cc16fcb2a80a.pdf |
| work_keys_str_mv | AT isargolzahi generalizingtheframeworkofdominyshabanilidarforthereduceddynamics |