Coin state properties in quantum walks

Abstract

Recent experimental advances have measured individual coin components in discrete time quantum walks, which have not received the due attention in most theoretical studies on the theme. Here is presented a detailed investigation of the properties of M, the difference between square modulus of coin states of discrete quantum walks on a linear chain. Local expectation values are obtained in terms of real and imaginary parts of the Fourier transformed wave function. A simple expression is found for the average difference between coin states in terms of an angle θ gauging the coin operator and its initial state. These results are corroborated by numerical integration of dynamical equations in real space. The local dependence is characterized both by large and short period modulations. The richness of revealed patterns suggests that the amount of information stored and retrieved from quantum walks is significantly enhanced if M is taken into account.