  When the interaction of a quantum system with a detector is changing from
weak to strong coupling limits, the system experiences a transition from the
regime with quantum mechanical coherent oscillations to the regime with a
frozen dynamics. In addition to this quantum Zeno transition, we show that the
full counting statistics of detector signal events experiences a topological
phase transition at the boundary between two phases at intermediate coupling of
a quantum system to the detector. We demonstrate that this transition belongs
to the class of topological phase transitions that can be classified by
elements of the braid group. We predict that this transition can be explored
experimentally by means of the optical spin noise spectroscopy.
