--- title: "Volichenko-type metasymmetry of braided Majorana qubits • 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/6ad2a767639f62b11adbd78e" 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_Volichenko-type%2Bmetasymmetry%2Bof%2Bbraided%2BMajorana%2Bqubits%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_F.%2BToppan%2Cdetalhe_~MTIvMDYvMjAyNA%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmQ3OGUi%2Cs_O8SGefIn4KPcoVKd.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Volichenko-type metasymmetry of braided Majorana qubits • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Volichenko-type%2Bmetasymmetry%2Bof%2Bbraided%2BMajorana%2Bqubits%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_F.%2BToppan%2Cdetalhe_~MTIvMDYvMjAyNA%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmQ3OGUi%2Cs_O8SGefIn4KPcoVKd.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Volichenko-type metasymmetry of braided Majorana qubits** **F. Toppan** 06/12/2024 [**Download PDF **1.2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbd78e/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Volichenko-type%20metasymmetry%20of%20braided%20Majorana%20qubits) ## **Publication details**
Authors
F. Toppan
Type
Physics Note
Status
Published
Publication date
12/06/2024
Description
This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits and clarifies their role; in particular, ``mixed-bracket" Heisenberg-Lie algebras are introduced. These algebras belong to a more general framework than the {\it Volichenko algebras} defined in 1990 by Leites-Serganova as {\it metasymmetries} which do not respect even/odd gradings and lead to mixed brackets interpolating ordinary commutators and anticommutators.\\ In a previous paper braided ${\mathbb Z}_2$-graded Majorana qubits were first-quantized within a graded Hopf algebra framework endowed with a braided tensor product. The resulting system admits truncations at roots of unity and realizes, for a given integer $s=2,3,4,\ldots$, an interpolation between ordinary Majorana fermions (recovered at $s=2$) and bosons (recovered in the $s\rightarrow \infty$ limit); it implements a parastatistics where at most $s-1$ indistinguishable particles are accommodated in a multi-particle sector.\\ The structures discussed in this work are:\\ - the quantum group interpretation of the roots of unity truncations recovered from a (superselected) set of reps of the quantum superalgebra ${\cal U}_q({\mathfrak{osp}}(1|2))$;\\ - the reconstruction, via suitable intertwining operators, of the braided tensor products as ordinary tensor products (in a minimal representation, the $N$-particle sector of the braided Majorana qubits is described by $2^N\times 2^N$ matrices);\\ - the introduction of mixed brackets for the braided creation/annihilation operators which define generalized Heisenberg-Lie algebras;\\ - the $s\rightarrow \infty$ untruncated limit of the mixed-bracket Heisenberg-Lie algebras producing parafermionic oscillators;\\ - ({\it meta})symmetries of ordinary differential equations given by matrix Schr\"{o}dinger equations in $0+1$ dimension induced by the braided creation/annihilation operators;\\ - in the special case of a third root of unity truncation, a nonminimal realization of the intertwining operators defines the system as a ternary algebra.
Year
2024
Number
CBPF-NF-002/24
Linked to a thesis
No
Linked to a grant
No
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