Paired Quantum Trajectories: Common Random Numbers for Protocol Selection in Continuously Monitored Quantum Systems
Abstract
A quantum jump trajectory is a discrete-event process in the literal sense: coherent evolution between jumps, a waiting time drawn from the decay of the no-jump norm, a channel selection at the jump. We take this correspondence in both directions. First, we build a monitored quantum laboratory (a driven emitter, detectors with efficiency and dead time, a click-driven feedback controller) inside a verification-first discrete-event engine that machine-checks the event structure and the bookkeeping on every transition, validated against exact finite-horizon renewal expectations and against QuTiP. Second, we import a comparison discipline that is standard in discrete-event simulation and that we did not find in the quantum trajectory literature: common random numbers. Addressing the randomness by event ordinal keeps two protocol arms on identical draws until their event histories diverge, and a mechanical audit verifies the pairing rather than assuming it. Pairing pays in proportion to trajectory alignment: for close protocol variants, where the selection decision is hard, the variance of the estimated protocol gap falls by a factor of 40 or more (replicated across five seeds), and the paired design resolves a 0.7% rate difference at $n = 400$ trajectories that the unpaired analysis of the same data cannot. Against the Fisher information of the click record, that paired design recovers about a tenth of the achievable precision at the count endpoint and the unpaired design under…
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