  Quantum walks can be used either as tools for quantum algorithm development
or as entanglement generators, potentially useful to test quantum hardware. We
present a novel algorithm based on a discrete Hadamard quantum walk on a line
with one coin and two walkers whose purpose is to generate entanglement between
walkers. We provide several classical computer simulations of our quantum
algorithm in which we show that, although the asymptotical amount of
entanglement generated between walkers does not reach the highest degree of
entanglement possible at each step for either coin measurement outcome, the
entanglement ratio (entanglement generated/highest value of entanglement
possible, for each step) tends to converge, and the actual convergence value
depends on the coin initial state and on the coin measurement outcome.
Furthermore, our numerical simulations show that, for the quantum walks used in
our algorithm, the value towards which entanglement ratio converges also
depends on the position probability distribution symmetry of a quantum walk
computed with one single walker and the same coin initial state employed in the
corresponding quantum walk with two walkers.
