Can a Pump-probe Experiment be Simulated Efficiently?

Measuring a quantum system disturbs its evolution. A pump-probe experiment is designed to monitor the autonomous dynamics of a quantum system between consecutive measurements. Modeling the evolution of observables in the pump-probe experiment is an essential ingredient of research in quantum dynamics.To be of practical importance the models should be amenable to efficient simulations on contemporary computers. This dissertation deals with the problem of efficient simulation of the pump-probe experiment. The number of independent observables of a quantum system having the effective Hilbert space dimensionN grows asN. In physically interesting applications that number of observables can be neither measured nor calculated. Therefore, a small subset of observables should be in the focus of an efficient dynamical simulation scheme. Commonly, the distinguished subset of observables considered in the context of efficient simulations is the subalgebra of local observables with respect to a given partition. The main obstacle on the way of efficient simulation of local dynamics is quantum entanglement. An initial pure state of a composite quantum system generically develops entanglement in the course of its unitary evolution. We propose and analyze two possible routes for quantum dynamics without entanglement: i) the initial mixed state unitary evolution and ii) an open system evolution of the composite system coupled locally to dephasing environment. Sufficient mixing of an initial state, measured by its temperature, is shown to result in the evolution with vanishing entanglement. Critical temperature for the crossover to the no-entanglement dynamical regime is calculated. An outline of the computation scheme for efficient simulation of the corresponding mixed state dynamics is presented. Coupling to local environment is believed to be generally detrimental to quantum entanglement. We have found that this view is incorrect. Certain types of local system-bath interactions can have a negligible effect on entanglement on the characteristic time-scale of the composite system purity decay. This is typical to an evolution of open systems, subjected to the Poissonian noise. On the other hand, local Gaussian noise is shown to be destructive to quantum entanglement. A local Gaussian noise has effect equivalent to a weak measurement of local observables of the composite quantum system. The destructive effect of the weak measurement on quantum entanglement can be attributed to the large time-scale separation between the decoherence of the density operator in a local basis and the dephasing of the composite system. In this sense the states in the corresponding local basis can be termed robust states. The robust states are suggested to