物理学报2017，Vol.66Issue(13)：31-40,10.DOI:10.7498/aps.66.130303
逾渗分立时间量子行走的传输及纠缠特性
Properties of distribution and entanglement in discrete-time quantum walk with percolation
摘要
Abstract
We investigate one-dimensional discrete-time quantum walk on the line where the links between neighboring sites are randomly broken. Two link-broken ways, static percolation and dynamical percolation, are considered. The former means that the broken links are fixed in position space at each time step, while the latter is that broken links are varied with time step. Our attention focuses on the effects of these disorders on two physical quantities, the probability distribution and the entanglement between the coin degree of freedom and position degree of freedom. Choosing Hadamard coin operator and assuming the walker to start from the position eigenstate |0〉 and attach itself to a coherent coin state 1/√2(|↑〉+i|↓〉), we give the statistical average results after making numerical calculations many times. The choices of coin operator and initial state, resulting in a symmetric probability distribution about origin in the ideal case, is helpful in comparing with different cases in different disorder strengths. It is shown that the probability distribution of static percolation quantum walk can change from a coherent behavior at short time to Anderson localization at longer time, while the dynamical percolation quantum walk can change to a classical diffusive behavior. With the decrease of the percolation probability, these transitions become faster. The entanglement for ideal case without disorder reaches a constant value after a short time evolution. The static percolation makes the entanglement less than that of ideal case and fluctuate irregularly around a certain value. The situation is very different for the dynamical percolation:the entanglement increases smoothly with the time step and can exceed the constant value in the ideal case at some time. Both of entanglements for two types of percolations decrease with reducing percolation probability. As a striking characteristic, the entanglement in dynamical case can tend to maximum regardless of percolation probability in long time limit, while the static case cannot. In the model for our study, the randomized unitary operations, induced by the static and dynamical percolations, can lead to some noticeable effects on the transport and entanglement of discrete time quantum walk. The results about the interplay between disorder and entanglement not only assist quantum information processing, but also give more options to further explore and understand disorder physical processes in nature.关键词
逾渗量子行走/概率分布/量子纠缠Key words
percolation quantum walk/probability distribution/quantum entanglement引用本文复制引用
安志云,李志坚..逾渗分立时间量子行走的传输及纠缠特性[J].物理学报,2017,66(13):31-40,10.基金项目
山西省回国留学人员科研资助项目(批准号: 2015-012)和山西省面上自然科学基金(批准号: 201601D011009)资助的课题. Project supported by Shanxi Scholarship Council of China (Grant No. 2015-012), and Natural Science Foundation of Shanxi Province, China (Grant No. 201601D011009). （批准号: 2015-012）
