  Qubit readout is commonly performed by thresholding a collection of analog
detector signals to obtain a sequence of single-shot bit values. The intrinsic
irreversibility of the mapping from analog to digital signals discards soft
information associated with an \emph{a posteriori} confidence that can be
assigned to each bit value when a detector is well characterized. Accounting
for soft information, we show significant improvements in enhanced state
detection with the quantum repetition code as well as quantum state or
parameter estimation. These advantages persist in spite of non-Gaussian
features of realistic readout models, experimentally relevant small numbers of
qubits, and finite encoding errors. These results show useful and achievable
advantages for a wide range of current experiments on quantum state tomography,
parameter estimation, and qubit readout.
