Abstract: Quantum walks are quantum analogons of random walks, the main difference of the definition of the two notion is that quantum walks can be described by a deterministic (quantum) evolution, thus the randomness emerges only at the time of observation. For coined quantum walks this behaviour originates from the extension of the walker's phase space by the so-called coin space, a usually low dimensional quantum system, and a unitary operator called coin operator. By this extension, the stochastic part of quantum walks -- choice of direction before each step, is eliminated. In the standard definition, at all sites the same coin operator is applied. Moving away from this restriction, a random, non-uniform distribution of coin operators give rise to disorder. In our recent research, we studied the effect of disorder on a quantum walk on a line. The coin operator belonging to SU(2) in this case can be characterised by 3 parameters. Depending on which parameters are varied, and the time scale of these variations one obtains: Anderson-type exponential localization, decoherence due to a depolarising channel, near-uniform distribution with linear spreading. These behaviours were also observed experimentally, using a fiber optical feedback loop with a delay line [1]. The non-uniform coin operators have been implemented by a controlled fast switching electro optical modulator.
[1] A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, Ch. Silberhorn, arXiv:1101.2638