多维连续时间量子随机游动的Itô公式

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Itô Formula for Multidimensional Continuous-Time Quantum Random Walk

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Kang Yuanbao. Itô Formula for Multidimensional Continuous-Time Quantum Random Walk[J].Acta mathematica scientia,Series A, 2016, 36(4): 771-782.

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[4] Fujita T. Random Walks and Stochastic Calculus (in Japanese). Tokyo: Nippon-Hyoron-Sha, 2008
[5] Konno N. A note on Itô's formula for discrete-time quantum walk. 2011, arXiv:1112.4335[quant-ph]
[6] Ampadu C. Itô's formula for the discrete-time quantum walk in two dimensions. Journal of Quantum Information Science, 2012, 2: 40-46
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[8] Mackay T D, Bartlett S D, Stephenson L T, Sanders B C. Quantum walks in higher dimensions. J Phys A: Math Gen, 2002, 35: 2745-2753
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[10] Konishi N, Konno N. Localization of two-dimensional quantum walks. Phys Rev A, 2004, 69: 052323
[11] Ko C K, Yoo H J. The generator and quantum Markov semigroup for quantum random walks. Kodai Math J, 2013, 36: 363-385
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[13] Muelken A, Blumen A. Quantum transport on two-dimensional regular graphs. J Phys A: Math Gen, 2006, 39: 14997-15012
[14] Yang W, Liu C, Zhang K. A path integral formula with applications to quantum random walks in Z^d. J Phys A: Math Theor, 2007, 40: 8487-8516
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[17] Biane P. Itô's stochastic calculus and Heisenberg commutation relations. Stochastic Process Appl, 2010, 120: 698-720
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