A generalized figure of merit for qubit readout

Many approaches to fault-tolerant quantum computation require repeated quantum nondemolition (QND) readout of qubits. A commonly used figure of merit for readout performance is the error rate for binary assignment in a single repetition. However, binary assignment discards important information on the level of confidence in the analog outcomes observed in real experiments. Here, a generalized figure of merit that fully captures the information contained in the analog readout outcomes, the Chernoff information, is proposed. Unlike the single-repetition error rate, the Chernoff information uniquely determines the cumulative error rate for arbitrary readout noise. Importantly, this universal description persists for the small number of repetitions and non-QND imperfections relevant to real experiments. In addition, the Chernoff information rigorously quantifies 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.