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Numerical method for finding decoherence-free subspaces and its applications

In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum channel. We prove that this algorithm will work for all cases with probability one, and it is more efficient than the algorithm proposed by Holbrook, Kribs, and Laflamme [Quant. Inf. Proc. 80, 381 (2003)]. In fact, our results reveal that this previous algorithm only works for special cases. As an application, we discuss how this method can be applied to increase the efficiency of an optimization procedure for finding an approximate DFS.