Transition in Splitting Probabilities of Quantum Walks
arXiv:2601.16111 · doi:10.1103/gvzq-n573
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 , where is the energy bandwidth, the splitting probability is universal and equal to , 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 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.
5 pages + 4 figures+ SM
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