Ergodic and mixing quantum channels in finite dimensions
The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of the channel is not a full-rank (faithful) density matrix. No...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2013-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/15/7/073045 |
| _version_ | 1797751436535136256 |
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| author | D Burgarth G Chiribella V Giovannetti P Perinotti K Yuasa |
| author_facet | D Burgarth G Chiribella V Giovannetti P Perinotti K Yuasa |
| author_sort | D Burgarth |
| collection | DOAJ |
| description | The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of the channel is not a full-rank (faithful) density matrix. Notably, we show that ergodicity is stable under randomizations, namely that every random mixture of an ergodic channel with a generic channel is still ergodic. In addition, we prove several conditions under which ergodicity can be promoted to the stronger property of mixing. Finally, exploiting a suitable correspondence between quantum channels and generators of quantum dynamical semigroups, we extend our results to the realm of continuous-time quantum evolutions, providing a characterization of ergodic Lindblad generators and showing that they are dense in the set of all possible generators. |
| first_indexed | 2024-03-12T16:48:30Z |
| format | Article |
| id | doaj.art-546a772687bc475e9e89059e3b6eac4f |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:48:30Z |
| publishDate | 2013-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-546a772687bc475e9e89059e3b6eac4f2023-08-08T11:27:20ZengIOP PublishingNew Journal of Physics1367-26302013-01-0115707304510.1088/1367-2630/15/7/073045Ergodic and mixing quantum channels in finite dimensionsD Burgarth0G Chiribella1V Giovannetti2P Perinotti3K Yuasa4Institute of Mathematics and Physics, Aberystwyth University , Physical Sciences Building, Penglais Campus, Aberystwyth, SY23 3BZ, UKCenter for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University , Beijing 100084, People's Republic of ChinaNEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR , Piazza dei Cavalieri 7, I-56126 Pisa, ItalyDipartimento di Fisica, Università degli Studi di Pavia and INFN Sezione di Pavia , Via Bassi 6, I-27100 Pavia, ItalyDepartment of Physics, Waseda University , Tokyo 169-8555, JapanThe paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of the channel is not a full-rank (faithful) density matrix. Notably, we show that ergodicity is stable under randomizations, namely that every random mixture of an ergodic channel with a generic channel is still ergodic. In addition, we prove several conditions under which ergodicity can be promoted to the stronger property of mixing. Finally, exploiting a suitable correspondence between quantum channels and generators of quantum dynamical semigroups, we extend our results to the realm of continuous-time quantum evolutions, providing a characterization of ergodic Lindblad generators and showing that they are dense in the set of all possible generators.https://doi.org/10.1088/1367-2630/15/7/073045 |
| spellingShingle | D Burgarth G Chiribella V Giovannetti P Perinotti K Yuasa Ergodic and mixing quantum channels in finite dimensions New Journal of Physics |
| title | Ergodic and mixing quantum channels in finite dimensions |
| title_full | Ergodic and mixing quantum channels in finite dimensions |
| title_fullStr | Ergodic and mixing quantum channels in finite dimensions |
| title_full_unstemmed | Ergodic and mixing quantum channels in finite dimensions |
| title_short | Ergodic and mixing quantum channels in finite dimensions |
| title_sort | ergodic and mixing quantum channels in finite dimensions |
| url | https://doi.org/10.1088/1367-2630/15/7/073045 |
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