We perform a finite-time scaling analysis over the detrapping point of a three-state quantum walk on the line. The coin operator is parametrized by $\rho$ that controls the wave packet spreading velocity. The input state prepared at the origin is set as a symmetric linear combination of two eigenstates of the coin operator with a characteristic mixing angle $\theta$, one of them being the component that results in full spreading occurring at ${\theta }_c\left(\rho \right)$ for which no fraction of the wave packet remains trapped near the initial position. We show that relevant quantities, such as the survival probability and the participation ratio assume single parameter scaling forms at the vicinity of the detrapping angle ${\theta }_c$. In particular, we show that the participation ratio grows linearly in time with a logarithmic correction, thus, shedding light on previous reports of sublinear behavior.

• Received 19 August 2021
• Revised 26 September 2021
• Accepted 15 October 2021

DOI:https://doi.org/10.1103/PhysRevE.104.054106