Deterministic Steering of Quantum Trajectories in the Generalized Rate Operator Formalism
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This thesis studies realization-dependent transformations in the generalized rate-operator quantum-jump formalism for open quantum systems. The aim is to examine whether these transformations can be used to steer the deterministic part of individual quantum trajectories toward a prescribed fixed target state, while preserving the physicality of the stochastic trajectories. This question is motivated by state-preparation tasks, where a quantum system must be driven to a known state quickly and with high probability, as in qubit resetting, qubit initialization, and the preparation of resourceful states. The theoretical part of the thesis introduces the basic framework of quantum mechanics, open quantum system dynamics, master equations, and stochastic quantum trajectories. The numerical part focuses on qubit dynamics and compares two examples: pure dephasing dynamics and Pauli master equation dynamics. For each fixed transformation, the simulations check the positivity condition, the attraction toward the target state, and the survival probability of the deterministic no-jump evolution. The results show that the simple fixed transformation considered for pure dephasing does not provide simultaneous attraction and positivity. In contrast, for Pauli master equation dynamics, fixed transformations are found that steer the deterministic trajectory toward the target while keeping the generalized rate operator positive. Because the isotropic Pauli master equation treats all directions on the Bloch sphere equally, the specific choice of the target state is just a reference direction, and the result carries over to any pure target state by symmetry. The survival probability analysis shows that steering can be achieved with quite high no-jump probability for the suitable parameter choices. The results suggest that realization-dependent transformations can provide useful trajectory level control in suitable open system dynamics.