Playing a true Parrondo's game with a three state coin on a quantum walk

A coin with three states is not necessarily an anomaly. A coin falls on either of its two sides head or tail. However, there is a remote possibility that it may not fall but roll on its edge and get stuck somewhere without falling on either of its sides. This possibility is remote for a classical coin so much so that it is never analyzed. For a three state quantum coin(qutrit), this is a fact. It has three states, period. Playing a Parrondo’s game with a qutrit is the subject of this paper. We show that a true quantum Parrondo’s game can be played with a 3 state coin in a 1D quantum walk in contrast to the fact that playing a true Parrondo’s game with a 2 state coin(qubit) in 1D quantum walk fails in the asymptotic limits.