Complexity of mixed Gaussian states from Fisher information geometry
Abstract We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2020)101 |
| _version_ | 1818363320922537984 |
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| author | Giuseppe Di Giulio Erik Tonni |
| author_facet | Giuseppe Di Giulio Erik Tonni |
| author_sort | Giuseppe Di Giulio |
| collection | DOAJ |
| description | Abstract We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices. |
| first_indexed | 2024-12-13T21:46:35Z |
| format | Article |
| id | doaj.art-7ffd4c1631ba4fad956277095d9b3292 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T21:46:35Z |
| publishDate | 2020-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-7ffd4c1631ba4fad956277095d9b32922022-12-21T23:30:23ZengSpringerOpenJournal of High Energy Physics1029-84792020-12-01202012110510.1007/JHEP12(2020)101Complexity of mixed Gaussian states from Fisher information geometryGiuseppe Di Giulio0Erik Tonni1SISSA and INFN — Sezione di TriesteSISSA and INFN — Sezione di TriesteAbstract We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.https://doi.org/10.1007/JHEP12(2020)101AdS-CFT CorrespondenceBlack HolesLattice Quantum Field Theory |
| spellingShingle | Giuseppe Di Giulio Erik Tonni Complexity of mixed Gaussian states from Fisher information geometry Journal of High Energy Physics AdS-CFT Correspondence Black Holes Lattice Quantum Field Theory |
| title | Complexity of mixed Gaussian states from Fisher information geometry |
| title_full | Complexity of mixed Gaussian states from Fisher information geometry |
| title_fullStr | Complexity of mixed Gaussian states from Fisher information geometry |
| title_full_unstemmed | Complexity of mixed Gaussian states from Fisher information geometry |
| title_short | Complexity of mixed Gaussian states from Fisher information geometry |
| title_sort | complexity of mixed gaussian states from fisher information geometry |
| topic | AdS-CFT Correspondence Black Holes Lattice Quantum Field Theory |
| url | https://doi.org/10.1007/JHEP12(2020)101 |
| work_keys_str_mv | AT giuseppedigiulio complexityofmixedgaussianstatesfromfisherinformationgeometry AT eriktonni complexityofmixedgaussianstatesfromfisherinformationgeometry |