Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form
This paper deals with the covariance matrix (CM) of two-mode Gaussian states, which, together with the mean vector, fully describes these states. In the two-mode states, the (ordinary) CM is a real symmetric matrix of order 4; therefore, it depends on 10 real variables. However, there is a very effi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/7/1485 |
| _version_ | 1797415316571029504 |
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| author | Gianfranco Cariolaro Roberto Corvaja |
| author_facet | Gianfranco Cariolaro Roberto Corvaja |
| author_sort | Gianfranco Cariolaro |
| collection | DOAJ |
| description | This paper deals with the covariance matrix (CM) of two-mode Gaussian states, which, together with the mean vector, fully describes these states. In the two-mode states, the (ordinary) CM is a real symmetric matrix of order 4; therefore, it depends on 10 real variables. However, there is a very efficient representation of the CM called the standard form (SF) that reduces the degrees of freedom to four real variables, while preserving all the relevant information on the state. The SF can be easily evaluated using a set of symplectic invariants. The paper starts from the SF, introducing an architecture that implements with primitive components the given two-mode Gaussian state having the CM with the SF. The architecture consists of a beam splitter, followed by the parallel set of two single–mode real squeezers, followed by another beam splitter. The advantage of this architecture is that it gives a precise non-redundant physical meaning of the generation of the Gaussian state. Essentially, all the relevant information is contained in this simple architecture. |
| first_indexed | 2024-03-09T05:46:58Z |
| format | Article |
| id | doaj.art-412319b311b541ad8248fed1d7756f9b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:46:58Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-412319b311b541ad8248fed1d7756f9b2023-12-03T12:20:24ZengMDPI AGSymmetry2073-89942022-07-01147148510.3390/sym14071485Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard FormGianfranco Cariolaro0Roberto Corvaja1Department of Information Engineering, University of Padova, 35122 Padova, ItalyDepartment of Information Engineering, University of Padova, 35122 Padova, ItalyThis paper deals with the covariance matrix (CM) of two-mode Gaussian states, which, together with the mean vector, fully describes these states. In the two-mode states, the (ordinary) CM is a real symmetric matrix of order 4; therefore, it depends on 10 real variables. However, there is a very efficient representation of the CM called the standard form (SF) that reduces the degrees of freedom to four real variables, while preserving all the relevant information on the state. The SF can be easily evaluated using a set of symplectic invariants. The paper starts from the SF, introducing an architecture that implements with primitive components the given two-mode Gaussian state having the CM with the SF. The architecture consists of a beam splitter, followed by the parallel set of two single–mode real squeezers, followed by another beam splitter. The advantage of this architecture is that it gives a precise non-redundant physical meaning of the generation of the Gaussian state. Essentially, all the relevant information is contained in this simple architecture.https://www.mdpi.com/2073-8994/14/7/1485continuous quantum variablesGaussian statescovariance matrixstandard form |
| spellingShingle | Gianfranco Cariolaro Roberto Corvaja Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form Symmetry continuous quantum variables Gaussian states covariance matrix standard form |
| title | Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form |
| title_full | Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form |
| title_fullStr | Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form |
| title_full_unstemmed | Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form |
| title_short | Implementation of Two-Mode Gaussian States Whose Covariance Matrix Has the Standard Form |
| title_sort | implementation of two mode gaussian states whose covariance matrix has the standard form |
| topic | continuous quantum variables Gaussian states covariance matrix standard form |
| url | https://www.mdpi.com/2073-8994/14/7/1485 |
| work_keys_str_mv | AT gianfrancocariolaro implementationoftwomodegaussianstateswhosecovariancematrixhasthestandardform AT robertocorvaja implementationoftwomodegaussianstateswhosecovariancematrixhasthestandardform |