A Clifford algebra of signature (n,3n) and the density operators of quantum information theory

Author(s)

Nolmar Melo

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2011-01-19

Examining board members

Carlile Campos Lavor; Sueli Irene Rodrigues Costa; Ricardo Antonio Mosna; Nelson Maculan Filho; Renato Portugal

• Advisor: Carlile Campos Lavor

Abstract

This work presents an algebraic language for two basic elements of quantum information theory (the quantum bits and density operators), based in the properties of a Clifford algebra of signature (n,3n). We prove that the new description of these elements preserves the same mathematical properties obtained with the classical description. We also extend some results presented in the literature that relate Clifford algebra and quantum information. (AU)