Advances in Applied Clifford Algebras

, Volume 26, Issue 2, pp 771–792 | Cite as

An Approach by Representation of Algebras for Decoherence-Free Subspaces

  • Marco A. S. Trindade
  • Eric Pinto
  • J. D. M. Vianna


The aim of this paper is to present a general algebraic formulation for the decoherence-free subspaces (DFSs). In order to build the DFSs we consider the tensor product of Clifford algebras and left minimal ideals. States, error operators and projection operators are defined in a purely algebraic point of view. For this purpose, we initially generalize some results of Pauli and Artin about semisimple algebras. Then we derive orthogonality theorems for associative algebras analogous to theorems for finite groups. Some advantages and perspectives are also discussed.


Clifford algebras Decoherence-free subspaces Quantum information 

Mathematics Subject Classification

15A66 81P40 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Marco A. S. Trindade
    • 1
  • Eric Pinto
    • 2
  • J. D. M. Vianna
    • 3
  1. 1.Departamento de Ciências Exatas e da TerraUniversidade do Estado da BahiaAlagoinhasBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal da BahiaSalvadorBrazil
  3. 3.Instituto de FísicaUniversidade Federal da BahiaSalvadorBrazil

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