  Many promising approaches to fault-tolerant quantum computation require
repeated quantum nondemolition (QND) readout of binary observables such as
quantum bits (qubits). A commonly used figure of merit for readout performance
is the error rate for binary assignment in a single repetition. However, it is
known that this figure of merit is insufficient. Indeed, real-world readout
outcomes are typically analog instead of binary. Binary assignment therefore
discards important information on the level of confidence in the analog
outcomes. Here, a generalized figure of merit that fully captures the
information contained in the analog readout outcomes is suggested. This figure
of merit is the Chernoff information associated with the statistics of the
analog readout outcomes in one repetition. Unlike the single-repetition error
rate, the Chernoff information uniquely determines the asymptotic cumulative
error rate for arbitrary readout noise. As a result, non-Gaussian readout noise
common in experiments can be described by effective Gaussian noise with the
same Chernoff information. Importantly, it is shown that such a universal
description persists for the small number of repetitions and non-QND
imperfections relevant to real experiments. Finally, the Chernoff information
is used to rigorously quantify the amount of information discarded by
analog-to-binary conversion. These results provide a unified framework for
qubit readout and should facilitate optimization and engineering of near-term
quantum devices across all platforms.
