Precision Reconstruction of Qudits Accounting for Readout Errors via the Confusion Matrix

We present a method for reconstructing multilevel quantum states (qudits) that explicitly accounts for readout errors. Our algorithm relies on the confusion matrix, treated as a stochastic transition matrix of a Markov chain. We pay special attention to the model with uniformly distributed errors and to the critical error probability at which the system completely loses the ability to reconstruct states. The reported results extend our earlier approach to high-precision control of qudits using fuzzy (unsharp) quantum measurements under decoherence.