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The average time $T$ required for high-fidelity readout of quantum states canbe significantly reduced via a real-time adaptive decision rule. An adaptivedecision rule stops the readout as soon as a desired level of confidence hasbeen achieved, as opposed to setting a fixed readout time $t_f$. Theperformance of the adaptive decision is characterized by the "adaptive-decisionspeedup," $t_f/T$. In this work, we reformulate this readout problem in termsof the first-passage time of a particle undergoing stochastic motion. Thisformalism allows us to theoretically establish the maximum achievableadaptive-decision speedups for several physical two-state readoutimplementations. We show that for two common readout schemes (the Gaussianlatching readout and a readout relying on state-dependent decay), the speedupis bounded by $4$ and $2$, respectively, in the limit of high single-shotreadout fidelity. We experimentally study the achievable speedup in areal-world scenario by applying the adaptive decision rule to a readout of thenitrogen-vacancy-center (NV-center) charge state. We find a speedup of $\approx2$ with our experimental parameters. In addition, we propose a simple readoutscheme for which the speedup can, in principle, be increased without bound asthe fidelity is increased. Our results should lead to immediate improvements innanoscale magnetometry based on spin-to-charge conversion of the NV-centerspin, and provide a theoretical framework for further optimization of thebandwidth of quantum measurements.

Maximal adaptive-decision speedups in quantum-state readout