Tomographic Universality of the Discrete Wigner Function
We observe that the discrete Wigner functions (DWFs) of <i>n</i>-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the <i>n</i>-qubit case, this property does not hold du...
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MDPI AG
2024-01-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/6/1/5 |
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| author | Isabel Sainz Ernesto Camacho Andrés García Andrei B. Klimov |
| author_facet | Isabel Sainz Ernesto Camacho Andrés García Andrei B. Klimov |
| author_sort | Isabel Sainz |
| collection | DOAJ |
| description | We observe that the discrete Wigner functions (DWFs) of <i>n</i>-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the <i>n</i>-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup. |
| first_indexed | 2024-04-24T17:53:19Z |
| format | Article |
| id | doaj.art-e51f8dd34094405188b860f510868e7e |
| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-04-24T17:53:19Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj.art-e51f8dd34094405188b860f510868e7e2024-03-27T14:01:51ZengMDPI AGQuantum Reports2624-960X2024-01-0161587310.3390/quantum6010005Tomographic Universality of the Discrete Wigner FunctionIsabel Sainz0Ernesto Camacho1Andrés García2Andrei B. Klimov3Departamento de Física, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, MexicoDepartamento de Matemáticas, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, MexicoDepartamento de Matemáticas, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, MexicoDepartamento de Física, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, MexicoWe observe that the discrete Wigner functions (DWFs) of <i>n</i>-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the <i>n</i>-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup.https://www.mdpi.com/2624-960X/6/1/5discrete Wigner functionquantum tomographystabilizer formalismmutually unbiased bases |
| spellingShingle | Isabel Sainz Ernesto Camacho Andrés García Andrei B. Klimov Tomographic Universality of the Discrete Wigner Function Quantum Reports discrete Wigner function quantum tomography stabilizer formalism mutually unbiased bases |
| title | Tomographic Universality of the Discrete Wigner Function |
| title_full | Tomographic Universality of the Discrete Wigner Function |
| title_fullStr | Tomographic Universality of the Discrete Wigner Function |
| title_full_unstemmed | Tomographic Universality of the Discrete Wigner Function |
| title_short | Tomographic Universality of the Discrete Wigner Function |
| title_sort | tomographic universality of the discrete wigner function |
| topic | discrete Wigner function quantum tomography stabilizer formalism mutually unbiased bases |
| url | https://www.mdpi.com/2624-960X/6/1/5 |
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