The Pauli Problem for Gaussian Quantum States: Geometric Interpretation
We solve the Pauli tomography problem for Gaussian signals using the notion of Schur complement. We relate our results and method to a notion from convex geometry, polar duality. In our context polar duality can be seen as a sort of geometric Fourier transform and allows a geometric interpretation o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/20/2578 |
| _version_ | 1797514003851771904 |
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| author | Maurice A. de Gosson |
| author_facet | Maurice A. de Gosson |
| author_sort | Maurice A. de Gosson |
| collection | DOAJ |
| description | We solve the Pauli tomography problem for Gaussian signals using the notion of Schur complement. We relate our results and method to a notion from convex geometry, polar duality. In our context polar duality can be seen as a sort of geometric Fourier transform and allows a geometric interpretation of the uncertainty principle and allows to apprehend the Pauli problem in a rather simple way. |
| first_indexed | 2024-03-10T06:25:28Z |
| format | Article |
| id | doaj.art-efec75529f1e4e73a796662abe269701 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:25:28Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-efec75529f1e4e73a796662abe2697012023-11-22T19:02:03ZengMDPI AGMathematics2227-73902021-10-01920257810.3390/math9202578The Pauli Problem for Gaussian Quantum States: Geometric InterpretationMaurice A. de Gosson0Faculty of Mathematics (NuHAG), University of Vienna, 1090 Vienna, AustriaWe solve the Pauli tomography problem for Gaussian signals using the notion of Schur complement. We relate our results and method to a notion from convex geometry, polar duality. In our context polar duality can be seen as a sort of geometric Fourier transform and allows a geometric interpretation of the uncertainty principle and allows to apprehend the Pauli problem in a rather simple way.https://www.mdpi.com/2227-7390/9/20/2578covriance matrixpolar dualityuncertainty principlereconstruction problem |
| spellingShingle | Maurice A. de Gosson The Pauli Problem for Gaussian Quantum States: Geometric Interpretation Mathematics covriance matrix polar duality uncertainty principle reconstruction problem |
| title | The Pauli Problem for Gaussian Quantum States: Geometric Interpretation |
| title_full | The Pauli Problem for Gaussian Quantum States: Geometric Interpretation |
| title_fullStr | The Pauli Problem for Gaussian Quantum States: Geometric Interpretation |
| title_full_unstemmed | The Pauli Problem for Gaussian Quantum States: Geometric Interpretation |
| title_short | The Pauli Problem for Gaussian Quantum States: Geometric Interpretation |
| title_sort | pauli problem for gaussian quantum states geometric interpretation |
| topic | covriance matrix polar duality uncertainty principle reconstruction problem |
| url | https://www.mdpi.com/2227-7390/9/20/2578 |
| work_keys_str_mv | AT mauriceadegosson thepauliproblemforgaussianquantumstatesgeometricinterpretation AT mauriceadegosson pauliproblemforgaussianquantumstatesgeometricinterpretation |