--- title: "Translations and reflections on the torus: Identities for discrete Wigner functions and transforms • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbcfd7" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~VHJhbnNsYXRpb25zIGFuZCByZWZsZWN0aW9ucyBvbiB0aGUgdG9ydXM6IElkZW50aXRpZXMgZm9yIGRpc2NyZXRlIFdpZ25lciBmdW5jdGlvbnMgYW5kIHRyYW5zZm9ybXM%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TWFyY29zIFNhcmFjZW5vOyBBLiBNLiBPem9yaW8gZGUgQWxtZWlkYQ%2Cdetalhe_~MTUvMDgvMjAxOA%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmNmZDci%2Cs_AMvTjkMQv1-kELKk.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Translations and reflections on the torus: Identities for discrete Wigner functions and transforms • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~VHJhbnNsYXRpb25zIGFuZCByZWZsZWN0aW9ucyBvbiB0aGUgdG9ydXM6IElkZW50aXRpZXMgZm9yIGRpc2NyZXRlIFdpZ25lciBmdW5jdGlvbnMgYW5kIHRyYW5zZm9ybXM%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TWFyY29zIFNhcmFjZW5vOyBBLiBNLiBPem9yaW8gZGUgQWxtZWlkYQ%2Cdetalhe_~MTUvMDgvMjAxOA%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmNmZDci%2Cs_AMvTjkMQv1-kELKk.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Translations and reflections on the torus: Identities for discrete Wigner functions and transforms** **Marcos Saraceno; A. M. Ozorio de Almeida** 08/15/2018 [**Download PDF **0.4 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbcfd7/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Translations%20and%20reflections%20on%20the%20torus%3A%20Identities%20for%20discrete%20Wigner%20functions%20and%20transforms) ## **Publication details**
Authors
Marcos Saraceno; A. M. Ozorio de Almeida
Type
Physics Note
Status
Published
Publication date
15/08/2018
Description
A finite Hilbert space can be associated to a periodic phase space, that is, a torus. A finite subgroup of operators corresponding to reflections and translations on the torus form respectively the basis for the discrete Weyl representation, including the Wigner function, and for its Fourier conjugate, the chord representation. They are invariant under Clifford transformations and obey analogous product rules to the continuous representations, so allowing for the calculation of expectations and correlations for observables. We here import new identities from the continuum for products of pure state Wigner and chord functions, involving, for instance the inverse phase space participation ratio and correlations of a state with its translate. New identities are derived involving transition Wigner or chord functions of transition operators |ψ1ψ2|. Extension of the reflection and translation operators to a doubled torus phase space leads to the representation of superoperators and so to the construction of the propagator of Wigner functions from the Weyl representation of the evolution operator.
Year
2018
Number
CBPF-NF-007/18
Linked to a thesis
No
Linked to a grant
No
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