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Limit Theorems for Open Quantum Random Walks

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Abstract

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 Schrödinger-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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Acknowledgement

This work was partially supported by the Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science (Grant No. 21540116).

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama, 240-8501, Japan

    Norio Konno

  2. Department of Applied Mathematics, Hankyong National University, 327 Jungangro, Anseong-si, Gyeonggi-do, 456-749, Korea

    Hyun Jae Yoo

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  1. Norio Konno
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  2. Hyun Jae Yoo
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Correspondence to Hyun Jae Yoo.

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Konno, N., Yoo, H.J. Limit Theorems for Open Quantum Random Walks. J Stat Phys 150, 299–319 (2013). https://doi.org/10.1007/s10955-012-0668-6

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  • DOI: https://doi.org/10.1007/s10955-012-0668-6

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