Splitting Probability for Monitored Quantum Systems

by Dr Prashant Singh (Bar Ilan University)

Thursday 7 May 2026, 11:30 → 12:30 Asia/Kolkata

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The splitting probability is a fundamental concept in the theory of stochastic processes and first-passage phenomena. It measures the probability that a stochastic trajectory reaches one designated target before any of the other available targets, thus providing a natural way to characterize competition between multiple possible outcomes. In this talk, I will discuss splitting probability in the context of monitored quantum systems. I will show that, in stark contrast to a classical random walk, the quantum splitting probability exhibits a nonanalytic, phase-transition-like behavior controlled by the sampling time at the targets. We also find the loss of the classical proximity effect and emergence of dark states which give rise to point-wise discontinuous transitions in the splitting probability. These results follow from a nontrivial mapping of the splitting problem onto a pair of single-target detection problems enabled by the superposition principle.