Information Dynamics In Controlled And Uncontrolled Quantum Systems

Harnessing quantum phenomena for technological applications relies heavily on preventing information 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 completed faster than decoherence times. Traditionally, the environment is viewed as a disruptive force; however, this perspective ignores the rich informational dynamics that environmental interactions 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 restructure 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 significantly 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 systems fully subject to environmental effects. Here, we investigate scenarios in which systems transition from pure quantum states to classically objective states as predicted by quantum Darwinism. 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 quantum information - decoherence and information scrambling. Information scrambling refers to the flow of initially accessible quantum information into complex many-body correlations with the system itself. Typical measures of scrambling used in closed systems fail to differentiate between the competing effects. We introduce a method for probing information scrambling even in the presence of open system effects, demonstrating that the environment not only acts as a sink for quantum information but also restructures the 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 environment on the structure of quantum information.