Recurrences in three-state quantum walks on a plane

被引:25
|
作者
Kollar, B. [2 ]
Stefanak, M. [1 ]
Kiss, T. [2 ]
Jex, I. [1 ]
机构
[1] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Dept Phys, CR-11519 Prague 1, Stare Mesto, Czech Republic
[2] Hungarian Acad Sci, Res Inst Solid State Phys & Opt, Dept Quantum Opt & Quantum Informat, H-1121 Budapest, Hungary
来源
PHYSICAL REVIEW A | 2010年 / 82卷 / 01期
关键词
LATTICE;
D O I
10.1103/PhysRevA.82.012303
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We analyze the role of dimensionality in the time evolution of discrete-time quantum walks through the example of the three-state walk on a two-dimensional triangular lattice. We show that the three-state Grover walk does not lead to trapping (localization) or recurrence to the origin, in sharp contrast to the Grover walk on the two-dimensional square lattice. We determine the power-law scaling of the probability at the origin with the method of stationary phase. We prove that only a special subclass of coin operators can lead to recurrence, and there are no coins that lead to localization. The propagation for the recurrent subclass of coins is quasi-one dimensional.
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页数:7
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