Operational geometric phase for mixed quantum states
The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove t...
| 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/10.1088/1367-2630/15/5/053006 |
| _version_ | 1797751555832676352 |
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| author | O Andersson H Heydari |
| author_facet | O Andersson H Heydari |
| author_sort | O Andersson |
| collection | DOAJ |
| description | The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics. |
| first_indexed | 2024-03-12T16:51:12Z |
| format | Article |
| id | doaj.art-023354c14942462e9d8c0183fc858c0f |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:51:12Z |
| publishDate | 2013-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-023354c14942462e9d8c0183fc858c0f2023-08-08T11:09:33ZengIOP PublishingNew Journal of Physics1367-26302013-01-0115505300610.1088/1367-2630/15/5/053006Operational geometric phase for mixed quantum statesO Andersson0H Heydari1Department of Physics, Stockholm University , SE-10691 Stockholm, SwedenDepartment of Physics, Stockholm University , SE-10691 Stockholm, SwedenThe geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics.https://doi.org/10.1088/1367-2630/15/5/053006 |
| spellingShingle | O Andersson H Heydari Operational geometric phase for mixed quantum states New Journal of Physics |
| title | Operational geometric phase for mixed quantum states |
| title_full | Operational geometric phase for mixed quantum states |
| title_fullStr | Operational geometric phase for mixed quantum states |
| title_full_unstemmed | Operational geometric phase for mixed quantum states |
| title_short | Operational geometric phase for mixed quantum states |
| title_sort | operational geometric phase for mixed quantum states |
| url | https://doi.org/10.1088/1367-2630/15/5/053006 |
| work_keys_str_mv | AT oandersson operationalgeometricphaseformixedquantumstates AT hheydari operationalgeometricphaseformixedquantumstates |