  Quantum polyspectra of up to fourth order are introduced for modeling and
evaluating quantum transport measurements offering a powerful alternative to
methods of the traditional full counting statistics. Experimental time-traces
of the occupation dynamics of a single quantum dot are evaluated via
simultaneously fitting their 2nd-, 3rd-, and 4th-order spectra. The scheme
recovers the same electron tunneling and spin relaxation rates as previously
obtained from an analysis of the same data in terms of factorial cumulants of
the full counting statistics and waiting-time distributions. Moreover, the
evaluation of time-traces via quantum polyspectra is demonstrated to be
feasible also in the weak measurement regime even when quantum jumps can no
longer be identified from time-traces and methods related to the full counting
statistics cease to be applicable. A numerical study of a double dot system
shows strongly changing features in the quantum polyspectra for the transition
from the weak measurement regime to the Zeno-regime where coherent tunneling
dynamics is suppressed. Quantum polyspectra thus constitute a general unifying
approach to the strong and weak regime of quantum measurements with possible
applications in diverse fields as nano-electronics, circuit quantum
electrodynamics, spin noise spectroscopy, or quantum optics.
