Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Influence of farmers educational level on comprehending, acting-upon and sharing of agro advisories

Although short messaging service (SMS) through mobile phones has quickly gained popularity among most other sectors in India, its potential is not fully realised in the agriculture sector as a cost effective service to reach farmers and elicit desirable action. Despite the cost effectiveness, mobile messaging has remained a challenge in the farming sector in terms of its end use and action as far as extension systems are concerned. While there could be many influencing factors affecting the utility of mobile messages, this study assumed that educational level of farmers could be a major factor. A telephone survey was conducted to ascertain the influence of farmers’ education on the level of utilisation of mobile-based advisories. Farmers with higher education level showed better comprehension of advisories, actedupon the advisories more promptly and shared the information with fellow farmers more often than those with lower education level. There was a significant association between comprehending, sharing and acting upon advisories. This has implications to achieve enhanced extension reach with higher efficiency in terms of cost and time.