Not All Probability Density Functions Are Tomograms
This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true p...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/3/176 |
| _version_ | 1797241161843212288 |
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| author | Liubov A. Markovich Justus Urbanetz Vladimir I. Man’ko |
| author_facet | Liubov A. Markovich Justus Urbanetz Vladimir I. Man’ko |
| author_sort | Liubov A. Markovich |
| collection | DOAJ |
| description | This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be “quantum”. |
| first_indexed | 2024-04-24T18:18:56Z |
| format | Article |
| id | doaj.art-3124db60bf6448b8b01e6b0760f4428d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-24T18:18:56Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3124db60bf6448b8b01e6b0760f4428d2024-03-27T13:36:46ZengMDPI AGEntropy1099-43002024-02-0126317610.3390/e26030176Not All Probability Density Functions Are TomogramsLiubov A. Markovich0Justus Urbanetz1Vladimir I. Man’ko2Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The NetherlandsInstituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The NetherlandsRussian Quantum Center, Skolkovo, Moscow 121205, RussiaThis paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be “quantum”.https://www.mdpi.com/1099-4300/26/3/176probability distribution functionsymplectic tomogramquantum state reconstructioncharacteristic function |
| spellingShingle | Liubov A. Markovich Justus Urbanetz Vladimir I. Man’ko Not All Probability Density Functions Are Tomograms Entropy probability distribution function symplectic tomogram quantum state reconstruction characteristic function |
| title | Not All Probability Density Functions Are Tomograms |
| title_full | Not All Probability Density Functions Are Tomograms |
| title_fullStr | Not All Probability Density Functions Are Tomograms |
| title_full_unstemmed | Not All Probability Density Functions Are Tomograms |
| title_short | Not All Probability Density Functions Are Tomograms |
| title_sort | not all probability density functions are tomograms |
| topic | probability distribution function symplectic tomogram quantum state reconstruction characteristic function |
| url | https://www.mdpi.com/1099-4300/26/3/176 |
| work_keys_str_mv | AT liubovamarkovich notallprobabilitydensityfunctionsaretomograms AT justusurbanetz notallprobabilitydensityfunctionsaretomograms AT vladimirimanko notallprobabilitydensityfunctionsaretomograms |