Markovian and non-Markovian state evolution in open quantum systems

Quantum states produced through parametric amplification with internal quantum noise are investigated. The internal diffusion arises by coupling both modes of light to a reservoir for the duration of the interaction time. The Wigner function for the diffused two-mode squeezed state is calculated. The nonlocality, separability, and purity of these quantum states of light are discussed. In addition, we study the nonlocality of two other continuous-variable states: the Werner state and the phase-diffused state for two light modes.; We examine stochastic maps in the context of quantum optics. Making use of the master equation, the damping basis, and the Bloch picture we calculate a non-unital, completely positive, trace-preserving map with unequal damping eigenvalues. This results in what we call the squeezed vacuum channel. A geometrical picture of the effect of stochastic noise on the set of pure state qubit density operators is provided. Finally, we study the capacity of the squeezed vacuum channel to transmit quantum information and to distribute EPR states.; The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. We examine master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. Using a stochastic process called the random telegraph signal, an analytical solution to such an equation is presented. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel.