  A notion of entangled Markov chain was introduced by Accardi and Fidaleo in
the context of quantum random walk. They proved that, in the finite dimensional
case, the corresponding states have vanishing entropy density, but they did not
prove that they are entangled.
  In the present note this entropy result is extended to the infinite
dimensional case under the assumption of finite speed of hopping. Then the
entanglement problem is discussed for spin 1/2, entangled Markov chains
generated by a binary symmetric channel with hopping probability $1-q$. The von
Neumann entropy of these states, restricted on a sublattice is explicitly
calculated and shown to be independent of the size of the sublattice. This is a
new, purely quantum, phenomenon.
  Finally the entanglement property between the sublattices ${\cal
A}(\{0,1,...,N\})$ and ${\cal A}(\{N+1\})$ is investigated using the PPT
criterium. It turns out that, for $q\neq 0,1,{1/2}$ the states are non
separable, thus truly entangled, while for $q=0,1,{1/2}$, they are separable.
