--- title: "Braided QM and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework • 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/6ad2a767639f62b11adbdaa2" 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_~QnJhaWRlZCBRTSBhbmQgTWFqb3JhbmEgcXViaXRzIGF0IHRoaXJkIHJvb3Qgb2YgdW5pdHk6IGEgY29sb3IgSGVpc2VuYmVyZy1MaWUgKHN1cGVyKWFsZ2VicmEgZnJhbWV3b3Jr%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Wmhhbm5hIEt1em5ldHNvdmE7IEYuIFRvcHBhbg%2Cdetalhe_~MDMvMTIvMjAyNQ%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmRhYTIi%2Cs_V-Ki4Gs9qWBaZrTv.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Braided QM and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QnJhaWRlZCBRTSBhbmQgTWFqb3JhbmEgcXViaXRzIGF0IHRoaXJkIHJvb3Qgb2YgdW5pdHk6IGEgY29sb3IgSGVpc2VuYmVyZy1MaWUgKHN1cGVyKWFsZ2VicmEgZnJhbWV3b3Jr%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Wmhhbm5hIEt1em5ldHNvdmE7IEYuIFRvcHBhbg%2Cdetalhe_~MDMvMTIvMjAyNQ%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmRhYTIi%2Cs_V-Ki4Gs9qWBaZrTv.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Braided QM and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework** **Zhanna Kuznetsova; F. Toppan** 12/03/2025 [**Download PDF **2.9 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbdaa2/pdf) [**Contact owner**]() ## **Publication details**
Authors
Zhanna Kuznetsova; F. Toppan
Type
Physics Note
Status
Published
Publication date
03/12/2025
Description
We introduce {\it color} Heisenberg-Lie (super)algebras graded by the abelian groups $\zthree^2$, $\ztwo^p\times\zthree^2$ for $p=1,2,3$, and investigate the properties of their associated multi-particle quantum paraoscillators.\par In the Rittenberg-Wyler's color Lie (super)algebras framework the above abelian groups are the simplest ones which induce {\it mixed brackets} interpolating commutators and anticommutators. These mixed brackets allow to accommodate two types of parastatistics: one based on the permutation group (beyond bosons and fermions in any space dimension) and an anyonic parastatistics based on the braid group. In both such cases the two broad classes of paraparticles are given by parabosons and parafermions.\par Mixed-bracket parafermions are created by nilpotent operators; they satisfy a generalized Pauli exclusion principle leading to roots-of-unity truncations in their multi-particle energy spectrum (braided Majorana qubits and their Gentile-type parastatistics are recovered in this color Lie superalgebra setting). \par Mixed-bracket parabosons do not admit truncations of the spectrum; the minimal detectable signature of their parastatistics is encoded in the measurable probability density of two indistinguishable parabosonic oscillators in a given energy eigenstate.
Year
2025
Number
CBPF-NF-003/25
Linked to a thesis
No
Linked to a grant
No
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