  The average time $T$ required for high-fidelity readout of quantum states can
be significantly reduced via a real-time adaptive decision rule. An adaptive
decision rule stops the readout as soon as a desired level of confidence has
been achieved, as opposed to setting a fixed readout time $t_f$. The
performance of the adaptive decision is characterized by the "adaptive-decision
speedup," $t_f/T$. In this work, we reformulate this readout problem in terms
of the first-passage time of a particle undergoing stochastic motion. This
formalism allows us to theoretically establish the maximum achievable
adaptive-decision speedups for several physical two-state readout
implementations. We show that for two common readout schemes (the Gaussian
latching readout and a readout relying on state-dependent decay), the speedup
is bounded by $4$ and $2$, respectively, in the limit of high single-shot
readout fidelity. We experimentally study the achievable speedup in a
real-world scenario by applying the adaptive decision rule to a readout of the
nitrogen-vacancy-center (NV-center) charge state. We find a speedup of $\approx
2$ with our experimental parameters. In addition, we propose a simple readout
scheme for which the speedup can, in principle, be increased without bound as
the fidelity is increased. Our results should lead to immediate improvements in
nanoscale magnetometry based on spin-to-charge conversion of the NV-center
spin, and provide a theoretical framework for further optimization of the
bandwidth of quantum measurements.
