  We analyze the quantum walk in higher spatial dimensions and compare
classical and quantum spreading as a function of time. Tensor products of
Hadamard transformations and the discrete Fourier transform arise as natural
extensions of the quantum coin toss in the one-dimensional walk simulation, and
other illustrative transformations are also investigated. We find that
entanglement between the dimensions serves to reduce the rate of spread of the
quantum walk. The classical limit is obtained by introducing a random phase
variable.

Quantum Physics