Abstract
A new kind of quantum random walks, called partially open quantum random walks (POQRW, for short), has been studied and developed by Sheng Xiong et al. in (J Stat Phys 152:473–492, 2013). In this paper, some properties of POQRW on the \({\mathbb {Z}}^{d}\) are obtained, to some extent, which extend the results of Ref (Sinayskiy in Phys Scr T151:4077, 2014). We obtain a central limit theorem and a large deviation principle for the position process \((X_{p})_{p\in {\mathbb {N}}}\) associated with the inhomogeneous POQRWs \(M^{m}_{p}(n)\) on the \({\mathbb {Z}}^{d}\), with internal space \(\hbar ={\mathbb {C}}^{2}\).
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Acknowledgements
This research is supported by the Natural Science Foundation of Chongqing(Grant No. csts2019jcyj-msxm0801)
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Kang, Y.B. On the properties of partially open quantum random walk on \({\mathbb {Z}}^{d}\). Quantum Inf Process 21, 62 (2022). https://doi.org/10.1007/s11128-021-03304-9
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DOI: https://doi.org/10.1007/s11128-021-03304-9