The bayesian learner is optimal for noisy binary search (and pretty good for quantum as well)

We use a Bayesian approach to optimally solve problems innoisy binary search. We deal with two variants:1. Each comparison is erroneous with independent probability 1-p.2. At each stage k comparisons can be performed in parallel and a noisy answer is returned.We present a (classical) algorithm which solves bothvariants optimally (with respect to p and k), up to an additive term of loglog n, and prove matching information-theoretic lower bounds. We use the algorithm to improve the results of Farhi et al. [FGGS99], presenting an exact quantum search algorithm in an ordered list of expected complexity less than log n / 3.