一维量子随机游动
Quantum random walks in one dimension
摘要：
这封信处理由2 × 2酉矩阵U确定的线上的量子随机行走。利用U给出的4个矩阵P、Q、R和S，给出了量子无规行走的m阶矩的组合表达式。阐明了m阶矩对U和初始量子比特态φ的依赖性。给出了量子行走的一类新的极限定理。进一步给出了量子行走分布对称的充分必要条件。结果表明，量子随机行走的行为与经典随机行走的行为有着显著的不同。
英文摘要：
This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The dependence of the mth moment on U and initial qubit state phi is clarified. A new type of limit theorems for the quantum walk is given. Furthermore necessary and sufficient conditions for symmetry of distribution for the quantum walk is presented. Our results show that the behavior of quantum random walk is striking different from that of the classical ramdom walk.
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