  Despite the coined quantum walk being a closed quantum system under a unitary
evolution, its Hilbert space can be divided in two sub-spaces, which makes it
possible for one to analyze one of the subsystems (the coin or the walker) as
an open system in contact with a reservoir. In the present work we calculate
the asymptotic reduced density matrix of the coin space of the three-state
quantum walk in an infinite line, and use that result to analyze the
entanglement between the chirality, and position space. We calculate the von
Neumann entropy and the entanglement temperature per mean energy of the system
in the asymptotic limit.
