Certifying the Rydberg-exposure limit of a globally driven controlled-Z gate

arXiv:2611.07388v1 Announce Type: new Abstract: Rydberg excitation enables entangling gates in neutral-atom quantum processors but also exposes them to spontaneous decay. Whether this exposure can be made arbitrarily small through pulse shaping and longer gate times has remained unresolved. We show that an exact controlled-$Z$ gate driven by a single global laser has an irreducible Rydberg-exposure cost in the perfect-blockade regime. The product of the maximum Rabi frequency $\Omega_{\max}$ and the average time $T_R$ spent in the Rydberg state is bounded below by $2.9312$, independent of pulse shape and duration. We derive this bound using a sum-of-squares certificate, strengthened by constraints imposed by the shared drive.