Quantum Walks with Entangled Coins

We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. Furthermore, we examine the numerical behaviour of such walks using Bell states as initial coin states, two different coin operators, two different shift operators, and one walker. We compare and contrast the performance of these quantum walks with that of a classical random walk consisting of one walker and two maximally correlated coins. We find the behavior of our walk with entangled coins can be very different in comparison to the usual quantum walk with a single coin. We also find that simply by changing the shift operator, we can generate widely different distributions