Monitored Recurrence of a One-parameter Family of Three-state Quantum
Walks
- URL: http://arxiv.org/abs/2212.00540v2
- Date: Mon, 27 Nov 2023 07:06:18 GMT
- Title: Monitored Recurrence of a One-parameter Family of Three-state Quantum
Walks
- Authors: Martin Stefanak
- Abstract summary: We show that the Polya number 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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