Coherence-gated quantum devices via real-time weak measurement

Single-photon routers in cavity and circuit QED direct photons based on which energy eigenstate a qubit occupies - a projective decision that destroys coherence. We propose coherence-gated routing, where the routing decision depends on the magnitude of quantum coherence, estimated in real time from simultaneous weak measurements of σ_x and σ_z. A photon is accepted depending on whether S(T) = sqrt{langleσ_xranglec² + langleσ_yranglec²} exceeds a tunable threshold S_th. Because coherence is certified at emission, the protocol enables two applications beyond conventional heralded sources: (i) a quantum random number generator with min-entropy bounded by Bloch-sphere geometry, H_infty geq -log_2bigl\(frac{1+sqrt{1-S_th²}}{2}bigr\), and (ii) a phase-tracked photon source where independent certification at two nodes bounds the matter-matter entanglement fidelity after Bell-state measurement. The real-time estimator is a security primitive, not merely a numerical tool. We benchmark seven configurations across 3000 trajectories and show that deliberately underestimating detector efficiency $η_a < η_true$ simultaneously stabilizes the numerics and suppresses overcertification. We trace this analytically through a purity monotonicity result, identify a geometric loophole amplifying purity undercertification into coherence overcertification by 45times, and develop two pointwise bounds: an Ornstein-Uhlenbeck comparison yielding 4.5\% operational overcertification validated at $3.6\%$ from $10⁶$ trajectories, and an exponential supermartingale establishing an exponential tail. The gap - a single polynomial optimization - defines a path to fully composable security.