Quantum measurements are commonly performed by thresholding a collection of analog detector-output 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 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/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.