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Center for Nonlinear Studies |
The information acquired during the monitoring of a quantum system provides a state descriptionthat can differ greatly from the description given by agents ignorant of the outcomes. While thelack 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 study the consequences of such measurement back-action to two problems in quantum theory: the derivation of 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 whichstandard quantum speed limits are violated, and we provide estimates for the range of velocitiesin an ensemble of realizations of continuous measurement records. We determine the dispersionof the speed of evolution and characterize the full statistics of single trajectories. Regarding the problem of spontaneous symmetry breaking, which is typically understood as a consequence ofrandom fluctuations 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. Unlike in the standard picture, our approach is dynamical and purely quantum mechanical in nature. We showthat, depending on the nature of the quantum monitoring, an observer can thus alter the topology and the pattern of symmetry breaking.
Host: Avadh Saxena