From classical to quantum information geometry: a guide for physicists
Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of quantum information geometry. First, the study of topological...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/aceb14 |
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| author | J Lambert E S Sørensen |
| author_facet | J Lambert E S Sørensen |
| author_sort | J Lambert |
| collection | DOAJ |
| description | Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of quantum information geometry. First, the study of topological phases of matter characterized by Chern number is rooted in the symplectic structure of the quantum state space, known in the physics literature as Berry curvature. Second, in the study of quantum phase transitions, the fidelity susceptibility has gained prominence as a universal probe of quantum criticality, even for systems that lack an obviously discernible order parameter. Finally, the study of quantum Fisher information in many body systems has seen a surge of interest due to its role as a witness of genuine multipartite entanglement and owing to its utility as a quantifier of quantum resources, in particular those useful in quantum sensing. Rather than a thorough review, our aim is to connect key results within a common conceptual framework that may serve as an introductory guide to the extensive breadth of applications, and deep mathematical roots, of quantum information geometry, with an intended audience of researchers in quantum many body and condensed matter physics. |
| first_indexed | 2024-03-12T16:55:12Z |
| format | Article |
| id | doaj.art-f82db594e12e4b35b9841a6f2060218d |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:55:12Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-f82db594e12e4b35b9841a6f2060218d2023-08-08T09:30:52ZengIOP PublishingNew Journal of Physics1367-26302023-01-0125808120110.1088/1367-2630/aceb14From classical to quantum information geometry: a guide for physicistsJ Lambert0https://orcid.org/0000-0002-0888-5582E S Sørensen1https://orcid.org/0000-0002-5956-1190Department of Physics & Astronomy, McMaster University , 1280 Main St. W., Hamilton, ON L8S 4M1, CanadaDepartment of Physics & Astronomy, McMaster University , 1280 Main St. W., Hamilton, ON L8S 4M1, CanadaRecently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of quantum information geometry. First, the study of topological phases of matter characterized by Chern number is rooted in the symplectic structure of the quantum state space, known in the physics literature as Berry curvature. Second, in the study of quantum phase transitions, the fidelity susceptibility has gained prominence as a universal probe of quantum criticality, even for systems that lack an obviously discernible order parameter. Finally, the study of quantum Fisher information in many body systems has seen a surge of interest due to its role as a witness of genuine multipartite entanglement and owing to its utility as a quantifier of quantum resources, in particular those useful in quantum sensing. Rather than a thorough review, our aim is to connect key results within a common conceptual framework that may serve as an introductory guide to the extensive breadth of applications, and deep mathematical roots, of quantum information geometry, with an intended audience of researchers in quantum many body and condensed matter physics.https://doi.org/10.1088/1367-2630/aceb14quantum Fisher informationquantum information geometrymultipartite entanglementquantum metrologyfidelity susceptibilityquantum variance |
| spellingShingle | J Lambert E S Sørensen From classical to quantum information geometry: a guide for physicists New Journal of Physics quantum Fisher information quantum information geometry multipartite entanglement quantum metrology fidelity susceptibility quantum variance |
| title | From classical to quantum information geometry: a guide for physicists |
| title_full | From classical to quantum information geometry: a guide for physicists |
| title_fullStr | From classical to quantum information geometry: a guide for physicists |
| title_full_unstemmed | From classical to quantum information geometry: a guide for physicists |
| title_short | From classical to quantum information geometry: a guide for physicists |
| title_sort | from classical to quantum information geometry a guide for physicists |
| topic | quantum Fisher information quantum information geometry multipartite entanglement quantum metrology fidelity susceptibility quantum variance |
| url | https://doi.org/10.1088/1367-2630/aceb14 |
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