The convergence of unitary quantum random walks

Belton, Alexander C. R. and Gnacik, Michal and Lindsay, J. Martin (2014) The convergence of unitary quantum random walks. Working Paper. UNSPECIFIED.

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Abstract

We give a simple and direct treatment of the convergence of quantum random walks to quantum stochastic operator cocycles, using the semigroup method. The pointwise product of two such quantum random walks is shown to converge to the quantum stochastic Trotter product of the respective limit cocycles. Since such Trotter products themselves reduce to pointwise products when the cocycles inhabit commuting subspaces of the system algebra, this yields an elementary approach to the quantum random walk approximation of the 'tensorisation' of cocycles with common noise dimension space. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.

Item Type:
Monograph (Working Paper)
Subjects:
ID Code:
69293
Deposited By:
Deposited On:
25 Apr 2014 12:50
Refereed?:
No
Published?:
Published
Last Modified:
27 May 2020 23:51