  This thesis examines seven topics in the areas of deterministic
open-quantum-system dynamics, quantum measurements, and quantum error
correction (QEC). The first topic concerns weak measurements and their
universality as a means of generating quantum operations. It is shown that
every generalized measurement can be implemented as a sequence of weak
(infinitesimal) measurements. The second topic is an application of this result
to the theory of entanglement. Necessary and sufficient differential conditions
for entanglement monotones are derived and are used to find a new entanglement
monotone for three-qubit states. The third topic is a study of the performance
of different master equations for the description of non-Markovian dynamics.
The system studied is a qubit coupled to a spin bath via the Ising interaction.
The fourth topic investigates continuous QEC in the presence of non-Markovian
noise. It is shown that due to the existence of a Zeno regime in non-Markovian
dynamics, the performance of continuous QEC exhibits a quadratic improvement
for a sufficiently high time resolution of the error-correcting operations. The
fifth topic studies the conditions for correctability of subsystem codes under
continuous dynamics. Necessary and sufficient conditions on the Lindbladian and
the system-environment Hamiltonian are derived. The sixth topic examines the
robustness of operator QEC codes against initialization errors. A new measure
of fidelity for encoded information is introduced and is used to show that
operator codes are robust against imperfect initialization without the need for
restriction of the standard operator QEC conditions. The last topic concerns
holonomic quantum computation (HQC) and stabilizer codes. A fault-tolerant
scheme for HQC is presented, proving the scalability of the holonomic approach.
