Consequences of measurement back-action from quantum monitoring: non-standard speed limits and spontaneous symmetry breaking

The information acquired during the monitoring of a quantum system provides a state description that can differ greatly from the description given by agents ignorant of the outcomes. While the lack of information in the later results in a mixed density matrix following open system dynamics, the measurement back-action in the former case provides a more accurate description. We present consequences of such measurement back-action to two problems in quantum theory: the limits to the speed of evolution, and the process of spontaneous symmetry breaking.
For the problem of the speed of evolution, we show that that there are trajectories for which standard quantum speed limits are violated, and determine the dispersion of the speed of evolution in an ensemble of realizations of continuous measurement records. Regarding the problem of spontaneous symmetry breaking, which is typically understood as a consequence of random uctuations either in the Hamiltonian governing the evolution or in the state of the system, we present a novel alternative mechanism, induced by the measurement back-action. We show that, depending on the nature of the quantum monitoring, an observer can alter the topology and the pattern of symmetry breaking.