2026-10-22 · arXiv Quantum Physics
arXiv:2610.29547v1 Announce Type: cross
Abstract: We consider a continuous-time quantum walk stroboscopically subjected to projective measurements on two distinct targets with sampling time period $\tau$. We construct a general renewal framework for the first-detection amplitude at each target, from which we obtain the associated splitting probabilities. For Hamiltonians with reflection symmetry, we further show that each dual-target first-detection amplitude can be viewed as an interference effect between a pair of single-target first-detection amplitudes. This formulation yields exact expressions for the splitting probabilities and gives special sampling times at which they undergo pointwise discontinuous jumps due to a form of ergodicity breaking associated with dark states. As an illustrative example, we apply the framework to a one-dimensional tight-binding lattice chain with nearest-neighbor hopping, and study the splitting probabilities as functions of the initial position and sampling time. Below a critical sampling time, $0
原文链接：https://arxiv.org/abs/2610.29547
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