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Limit theorems for open quantum random walks

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arxiv 1209.1419 v1 pith:AH4JAM7Q submitted 2012-09-06 math-ph math.MPquant-ph

Norio Konno , Hyun Jae Yoo This is my paper · ORCID
classification math-phmath.MPquant-ph
keywords quantumlimitopenrandomwalksconsiderdistributionsprocess
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We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of Schr\"odinger-Heisenberg representation in quantum mechanics. By this, we can compute the distribution of the open quantum random walks concretely for many examples and thereby we can also obtain the limit distributions of them. In particular, it is possible to get rid of the initial state when we consider the evolution of the walk, it appears only in the last step of the computation.

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  1. Lazy Open Quantum Walks

    quant-ph 2019-08 conditional novelty 5.0 of 10

    Lazy open quantum walks on a d-dimensional lattice converge to a Gaussian distribution, with an explicit covariance formula that matches a direct numerical simulation.

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