  Quantum walk models have been used as an algorithmic tool for quantum
computation and to describe various physical processes. This paper revisits the
relationship between relativistic quantum mechanics and the quantum walks. We
show the similarities of the mathematical structure of the decoupled and
coupled form of the discrete-time quantum walk to that of the Klein-Gordon and
Dirac equations, respectively. In the latter case, the coin emerges as an
analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled
form of the continuous-time quantum walk is also shown by transforming the
decoupled form of the discrete-time quantum walk to the Schrodinger form. By
showing the coin to be a means to make the walk reversible, and that the
Dirac-like structure is a consequence of the coin use, our work suggests that
the relativistic causal structure is a consequence of conservation of
information. However, decoherence (modelled by projective measurements on
position space) generates entropy that increases with time, making the walk
irreversible and thereby producing an arrow of time. Lieb-Robinson bound is
used to highlight the causal structure of the quantum walk to put in
perspective the relativistic structure of quantum walk, maximum speed of the
walk propagation and the earlier findings related to the finite spread of the
walk probability distribution. We also present a two-dimensional quantum walk
model on a two state system to which the study can be extended.
