Harnessing quantum phenomena for technological applications relies heavily on preventing infor- mation loss through decoherence. To prevent this loss, it is crucial to develop strategies that enable the rapid and precise control of quantum systems, ensuring that desired processes are com- pleted faster than decoherence times. From a control perspective, the environment is viewed as a disruptive force; however, this ignores the rich informational dynamics that interactions with an environment can induce. By relaxing the requirement for strict control and adopting a more active treatment of the environment, this thesis explores how these dynamics contribute to the emergence of classicality from quantum mechanics, and how it can change the internal information structure in quantum many-body systems.
The study begins by addressing the challenges of controlling quantum systems near critical points, where conventional adiabatic methods become inefficient due to closing energy gaps. We propose a novel control strategy that applies counterdiabatic driving selectively within the impulse regime, as recognised by the Kibble-Zurek mechanism. This reduces energetic costs while maintaining high fidelity. This approach is validated both numerically and analytically, demonstrating substantial energetic savings.
Next, we explore control strategies relevant to implementing unitary gates in two distinct physical settings. The first involves analytically determining a Hamiltonian that achieves gate operations with unit fidelity without external control, while the second leverages an auxiliary qubit that requires external driving. Despite the latter scheme being more resource intensive, we show that the additional complexity of driving and controlling an auxiliary qubit can be advantageous when we subject the systems to decoherence.
Moving beyond controlled systems, we examine the informational dynamics of quantum sys- tems subject to the influence of their environment. Here, we investigate scenarios in which systems transition from pure quantum states to classically objective states as predicted by quantum Dar- winism. By partitioning the environment into accessible and inaccessible parts, we reveal how the interplay between these partitions determines whether classical objectivity emerges or if the system equilibrates without the redundant encoding of the state of the system into the environment.
Finally, we explore the competition between two sinks for local quantum information - decoher- ence and information scrambling. Information scrambling refers to the flow of initially accessible quantum information into complex many-body correlations within the system itself. Typical mea- sures of scrambling used in closed systems can fail to differentiate between the local information spreading throughout the degrees of freedom of the systems and the spreading of information due to decoherence. We introduce a method for probing information scrambling even in the presence of open system effects, demonstrating that the environment restructures remaining information, reducing the complexity of the system’s dynamics.
Collectively, these findings provide a comprehensive framework for understanding information dynamics in open quantum systems, offering new strategies for preserving quantum coherence and diagnosing the impact of an environment on the structure of quantum information.