STEERING THE QUANTUM: FROM REMOTE STATE PREPARATION TO QUANTUM TRANSPORT

Quantum information science is a vast and rapidly developing field of research in physics, which accompanies and partially guides the parallel development of quantum technologies, with the common goal of harnessing quantum phenomena to achieve tasks that are classically unfeasible or to greatly improve current technological strategies. It can be broadly identified through a general feature: a contribution to quantum information science usually entails a fine control of quantum degrees of freedom, be it direct or not, which is uncommon in all other branches of physics exploiting quantum mechanics: experimental violations of Bell’s inequalities, quantum teleportation and transport, quantum computation and essentially all topics in quantum information require a true control of quantum states and they often unveil the unperceived details of the quantum nature underlying everyday experience. Because of this intersectional character, it finds application in a wide spectrum of modern physical research, encompassing cosmology, black holes physics, solid state physics, quantum computation, foundational questions on the quantum theory itself and it even propels and inspires the development of better classical algorithms. Of paramount importance in quantum information science is the ability to prepare desirable quantum states and to steer their evolution in a predictable, tuneable and useful way. This thesis would aspire to contribute to an infinitesimal development towards these goals. After an introductory overview of the basic tools, in Part I we discuss continuous-variable quantum information with a focus on Gaussian steering and quantum metrology, the first relating to the remote preparation of quantum states and properties, P-nonclassicality in particular, and the second as the most important tool to characterize quantum systems. In Part II, the different approach of attaining target quantum states on discrete structures through continuous-time quantum walks is undertaken and several recent results on chiral quantum walks are presented cohesively, together with a physical intuition for these systems.