On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced a class of q...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/3/3/31 |
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| author | Charlyne de Gosson Maurice de Gosson |
| author_facet | Charlyne de Gosson Maurice de Gosson |
| author_sort | Charlyne de Gosson |
| collection | DOAJ |
| description | It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced a class of quantum states for which this property is satisfied; these states are dubbed “Feichtinger states” because they are defined in terms of a class of functional spaces (modulation spaces) introduced in the 1980s by H. Feichtinger. The properties of these states were studied, giving us the opportunity to prove an extension to the general case of a result due to Jaynes on the non-uniqueness of the statistical ensemble, generating a density operator. |
| first_indexed | 2024-03-10T07:16:10Z |
| format | Article |
| id | doaj.art-2b6b2f664f5a470dad20f4288716121b |
| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-10T07:16:10Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj.art-2b6b2f664f5a470dad20f4288716121b2023-11-22T15:01:57ZengMDPI AGQuantum Reports2624-960X2021-08-013347348110.3390/quantum3030031On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner DistributionCharlyne de Gosson0Maurice de Gosson1Faculty of Mathematics (NuHAG), University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, AustriaFaculty of Mathematics (NuHAG), University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, AustriaIt is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced a class of quantum states for which this property is satisfied; these states are dubbed “Feichtinger states” because they are defined in terms of a class of functional spaces (modulation spaces) introduced in the 1980s by H. Feichtinger. The properties of these states were studied, giving us the opportunity to prove an extension to the general case of a result due to Jaynes on the non-uniqueness of the statistical ensemble, generating a density operator.https://www.mdpi.com/2624-960X/3/3/31mixed statecovariance matrixWigner distributionmodulation space |
| spellingShingle | Charlyne de Gosson Maurice de Gosson On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution Quantum Reports mixed state covariance matrix Wigner distribution modulation space |
| title | On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution |
| title_full | On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution |
| title_fullStr | On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution |
| title_full_unstemmed | On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution |
| title_short | On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution |
| title_sort | on the non uniqueness of statistical ensembles defining a density operator and a class of mixed quantum states with integrable wigner distribution |
| topic | mixed state covariance matrix Wigner distribution modulation space |
| url | https://www.mdpi.com/2624-960X/3/3/31 |
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