| In this thesis we consider different approaches to quantifying the degree of decoherence by single numerical measures, derived from the full set of the density matrix elements. We identify a new measure of decoherence based on the operator norm. This measure can be shown to have several useful features. Its behavior as a function of time has no dependence on the initial conditions, and is expected to be insensitive to the internal dynamical time scales of the system, thus only probing the decoherence-related time dependence. For a spin-boson model---a prototype of a qubit interacting with environment---we also demonstrate the property of additivity, even if the qubits are entangled, as expected in quantum-computing applications.; We apply this approach to analyze decoherence of an electron in a double-dot, which was recently proposed as a candidate for the semiconductor charge qubit, due to the interaction with acoustic phonons. It is demonstrated that in common semiconductors, such as Si and GaAs, the error rate due to acoustic phonons is of the order of the fault-tolerance threshold and the dephasing mechanism determines the lower limit for the qubit decoherence measure.; Following the recent experiment in decoherence of entangled many-particle systems we consider the problem of the dipole-dipole decoherence of nuclear spins for a strongly correlated spin cluster. Our results show that its dynamics can be described as decoherence due to interaction with a composite bath consisting of fully correlated and uncorrelated parts. The decoherence rate scales up as a square root of the number of spins giving the linear scaling of the resulting error. Our theory is consistent with reported experimental data and previous theoretical findings.; Finally we consider the problem of current generation in a quantum wire due to external electromagnetic radiation. The photocurrent is caused by the interplay of the spin-orbit interaction and external in-plane magnetic field. The magnitude and the direction of the current depend on the Dresselhaus and Rashba constants, strength of magnetic field, radiation frequency and intensity. Material parameters, such as spin-orbit coupling constants, can be obtained from the analysis of the photocurrent. |
