  The blinking statistics of quantum emitters and their corresponding Markov
models play an important role in high resolution microscopy of biological
samples as well as in nano-optoelectronics and many other fields of science and
engineering. Current methods for analyzing the blinking statistics like the
full counting statistics or the Viterbi algorithm break down for low photon
rates. We present an evaluation scheme that eliminates the need for both a
minimum photon flux and the usual binning of photon events which limits the
measurement bandwidth. Our approach is based on higher order spectra of the
measurement record which we model within the recently introduced method of
quantum polyspectra from the theory of continuous quantum measurements. By
virtue of this approach we can determine on- and off-switching rates of a
semiconductor quantum dot at light levels 1000 times lower than in a standard
experiment and 20 times lower than achieved with a scheme from full counting
statistics. Thus a very powerful high-bandwidth approach to the parameter
learning task of single photon hidden Markov models has been established with
applications in many fields of science.
