  A new model that maps a quantum random walk described by a Hadamard operator
to a particular case of a random walk is presented. The model is represented by
a Markov chain with a stochastic matrix, i.e., all the transition rates are
positive, although the Hadamard operator contains negative entries. Using a
proper transformation that is applied to the random walk distribution after n
steps, the probability distributions in space of the two quantum states |1>,
|0> are revealed. These show that a quantum walk can be entirely mapped to a
particular case of a higher dimension of a random walk model. The random walk
model and its equivalence to a Hadamard walk can be extended for other cases,
such as a finite chain with two reflecting points

Quantum Physics