Quantum random walk approximation in Banach algebra

Das, B. Krishna and Lindsay, J. Martin (2015) Quantum random walk approximation in Banach algebra. Journal of Mathematical Analysis and Applications, 430 (1). pp. 465-482. ISSN 0022-247X

Abstract

Abstract Belton's discrete approximation scheme is extended to Banach-algebra-valued sesquilinear quantum stochastic cocycles, through the dyadic discretisation of time. Approximation results for Markov-regular quantum stochastic mapping cocycles are recovered. We also obtain a new random walk approximation for a class of (not necessarily Markov-regular) isometric operator cocycles. Every Lévy process on a compact quantum group is implemented by a unitary cocycle from this class.