Monitored recurrence of a one-parameter family of three-state quantum walks

Monitored recurrence of a one-parameter set of three-state quantum walks on a line is investigated. The calculations are considerably simplified by choosing a suitable basis of the coin space. We show that the Polya number (i.e. the site recurrence probability) depends on the coin parameter and the probability that the walker is initially in a particular coin state for which the walk returns to the origin with certainty. Finally, we present a brief investigation of the exact quantum state recurrence.

Automated summary

This paper investigates the monitored recurrence of a one-parameter set of three-state quantum walks on a line. The calculations are simplified by choosing a suitable basis of the coin space. The study shows that the Polya number depends on the coin parameter and the probability of the walker being initially in a specific coin state where the walk returns to the origin with certainty. Finally, a brief investigation of the exact quantum state recurrence is presented.