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arXiv · 2601.16111

Transition in Splitting Probabilities of Quantum Walks

Prashant Singh·David A. Kessler·Eli Barkai
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Abstract

We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the sampling time at the targets. For large systems and sampling times smaller than a critical value $\tau_c = 2\pi/\Delta E$, where $\Delta E$ is the energy bandwidth, the splitting probability is universal and equal to $1/2$, independent of the initial condition and the sampling time. Above the critical sampling time, a nonuniversal regime emerges in which the splitting probability deviates from $1/2$ and develops a fluctuating pattern of pronounced peaks and dips dependent on both the sampling time and the initial condition. These results follow from a nontrivial mapping of the splitting problem onto a pair of single-target detection problems enabled by the superposition principle.

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Prashant Singh, David A. Kessler, Eli Barkai. 2026-01-22. Transition in Splitting Probabilities of Quantum Walks. https://doi.org/10.1103/gvzq-n573

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