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An Approach by Representation of Algebras for Decoherence-Free Subspaces

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Ciências Exatas e da Terra, Universidade do Estado da Bahia, Alagoinhas, BA, 48040-210, Brazil

    Marco A. S. Trindade

  2. Departamento de Matemática, Universidade Federal da Bahia, Salvador, BA, 40210-340, Brazil

    Eric Pinto

  3. Instituto de Física, Universidade Federal da Bahia, Salvador, BA, 40210-340, Brazil

    J. D. M. Vianna

Authors
  1. Marco A. S. Trindade
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  2. Eric Pinto
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  3. J. D. M. Vianna
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Correspondence to Eric Pinto.

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Trindade, M.A.S., Pinto, E. & Vianna, J.D.M. An Approach by Representation of Algebras for Decoherence-Free Subspaces. Adv. Appl. Clifford Algebras 26, 771–792 (2016). https://doi.org/10.1007/s00006-015-0623-0

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