1203.5396 (Takuya Machida)

Limit theorem for discrete-time quantum walks on the line with binomial
initial states    [PDF]

Takuya Machida

Many limit theorems for discrete-time quantum walks starting with localized state have been investigated and some experiments corresponding to the quantum walks are realized. On the other hand, there is not limit theorem for quantum walks whose initial state is widely distributed over a domain. Long-time limit theorem plays an important role in expressing the asymptotic behavior of quantum walkers after many steps. In this work, we present a new limit theorem for discrete-time 2-state quantum walks initially prepared in wider probability amplitude distributions determined by binomial coefficients. Our result is significant in realizations of quantum walks, because it is difficult to set a quantum particle exactly localized eigenstate according to uncertainty principle.

View original: http://arxiv.org/abs/1203.5396