Reading qubits with sequential weak measurements: limits of information extraction

We study the information physics of quantum trajectories based on weak measurements in order to address the optimal achievable performance in qubit configuration readout for two realistic models of single qubit readout: (i) Model I is informationally complete, but without intrinsic dynamics; (ii) Model II is informationally incomplete weak measurements with intrinsic dynamics. We use mutual information (MI) to characterize how much information about the initial state is encoded in the measurement record. Using a fixed discrete time-step formulation, we compute the MI while varying the measurement strength, duration of measurement record, and the relative strength of intrinsic dynamics in our measurement schemes. We observe and exploit the emergence of continuum scaling and the Stochastic master equation in the weak measurement limit. We develop a perturbative analytic expansion in the measurement efficiency parameter to calculate MI, which captures qualitative and quantitative features of the numerical data. Both models exhibit clear bounds on information extraction as limiting values of the scaling function. Our analysis obtains these bounds and also flags optimal conditions on measurement strength and/or duration required to saturate them, as determined by intrinsic precessional dynamics (in Model II). Our results should be useful both for quantum device operation and optimization and also, possibly, for improving the performance of recent machine learning approaches for qubit and multiqubit configuration readout in current Noisy intermediate-scale quantum experiment regimes.