Particle approximations of Wigner distributions for n arbitrary observables
A class of signed joint probability measures for n arbitrary quantum observables is derived and studied based on quasicharacteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner distribution associated with these observables can be rigorously appro...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013102 |
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| _version_ | 1832584198214385664 |
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| author | Ralph Sabbagh Olga Movilla Miangolarra Hamid Hezari Tryphon T. Georgiou |
| author_facet | Ralph Sabbagh Olga Movilla Miangolarra Hamid Hezari Tryphon T. Georgiou |
| author_sort | Ralph Sabbagh |
| collection | DOAJ |
| description | A class of signed joint probability measures for n arbitrary quantum observables is derived and studied based on quasicharacteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner distribution associated with these observables can be rigorously approximated by such measures. These measures are given by affine combinations of Dirac delta distributions supported over the finite spectral range of the quantum observables and give the correct probability marginals when coarse-grained along any principal axis. We specialize to bivariate quasiprobability distributions for the spin measurements of spin-1/2 particles and derive their closed-form expressions. As a side result, we point out a connection between the convergence of these particle approximations and the Mehler-Heine theorem. Finally, we interpret the supports of these quasiprobability distributions in terms of repeated thought experiments. |
| format | Article |
| id | doaj-art-ad0b048fae5e42d28f00c42f975d77e0 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-ad0b048fae5e42d28f00c42f975d77e02025-01-27T15:07:46ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-017101310210.1103/PhysRevResearch.7.013102Particle approximations of Wigner distributions for n arbitrary observablesRalph SabbaghOlga Movilla MiangolarraHamid HezariTryphon T. GeorgiouA class of signed joint probability measures for n arbitrary quantum observables is derived and studied based on quasicharacteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner distribution associated with these observables can be rigorously approximated by such measures. These measures are given by affine combinations of Dirac delta distributions supported over the finite spectral range of the quantum observables and give the correct probability marginals when coarse-grained along any principal axis. We specialize to bivariate quasiprobability distributions for the spin measurements of spin-1/2 particles and derive their closed-form expressions. As a side result, we point out a connection between the convergence of these particle approximations and the Mehler-Heine theorem. Finally, we interpret the supports of these quasiprobability distributions in terms of repeated thought experiments.http://doi.org/10.1103/PhysRevResearch.7.013102 |
| spellingShingle | Ralph Sabbagh Olga Movilla Miangolarra Hamid Hezari Tryphon T. Georgiou Particle approximations of Wigner distributions for n arbitrary observables Physical Review Research |
| title | Particle approximations of Wigner distributions for n arbitrary observables |
| title_full | Particle approximations of Wigner distributions for n arbitrary observables |
| title_fullStr | Particle approximations of Wigner distributions for n arbitrary observables |
| title_full_unstemmed | Particle approximations of Wigner distributions for n arbitrary observables |
| title_short | Particle approximations of Wigner distributions for n arbitrary observables |
| title_sort | particle approximations of wigner distributions for n arbitrary observables |
| url | http://doi.org/10.1103/PhysRevResearch.7.013102 |
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