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Clifford algebras, algebraic spinors, quantum information and applications

Colegiado de Física, Departamento de Ciências Exatas e da Terra, Universidade do Estado da Bahia Salvador, Bahia 41150-000, Brazil

E-mail Address: matrindade@uneb.br

Corresponding author.

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Sergio Floquet

Colegiado de Engenharia Civil, Universidade Federal do Vale do São Francisco, Juazeiro, Bahia 48902-300, Brazil

E-mail Address: sergio.floquet@univasf.edu.br

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J. David M. Vianna

Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia 40170-280, Brazil

Instituto de Física, Universidade de Brasília, Brasília, Distrito Federal 70919-970, Brazil

E-mail Address: jdavid@fis.unb.br

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https://doi.org/10.1142/S0217732320502399Cited by:1 (Source: Crossref)

Abstract

We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored in connection with states of qubits. Supersymmetry and M-superalgebra are also analyzed with our formalism. Specifically we use extensively the algebras $C l_{3, 0}$ and $C l_{1, 3}$ as well as tensor products of Clifford algebras.

Keywords:

PACS: 03.65.Fd, 03.67.Lx, 02.10.Hh

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