Matrix Valued Szeg ˝ O Polynomials and Quantum Random Walks

@inproceedings{GrnbaumMatrixVS,
  title={Matrix Valued Szeg ˝ O Polynomials and Quantum Random Walks},
  author={F. Alberto Gr{\"u}nbaum}
}
We consider quantum random walks (QRW) on the integers, a subject that has been considered in the last few years in the framework of quantum computation. We show how the theory of CMV matrices gives a natural tool to study these processes and to give results that are analogous to those that Karlin and McGregor developed to study (classical) birth-and-death processes using orthogonal polynomials on the real line. In perfect analogy with the classical case the study of QRWs on the set of non… CONTINUE READING

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