  We present a mathematical formalism for the description of unrestricted
quantum walks with entangled coins and one walker. The numerical behaviour of
such walks is examined when using a Bell state as the initial coin state, 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 as well as quantum walks with coins sharing different degrees of
entanglement.
  We illustrate that the behaviour of our walk with entangled coins can be very
different in comparison to the usual quantum walk with a single coin. We also
demonstrate that simply by changing the shift operator, we can generate widely
different distributions. We also compare the behaviour of quantum walks with
maximally entangled coins with that of quantum walks with non-entangled coins.
Finally, we show that the use of different shift operators on 2 and 3 qubit
coins leads to different position probability distributions in 1 and 2
dimensional graphs.
