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.

Transaction costs of farmers’ participation in forest management: Policy implications of payments for environmental services schemes in Vietnam

Recent research on payments for environmental services (PES) has observed that high transaction costs (TCs) are incurred through the implementation of PES schemes and farmer participation. TCs incurred by households are considered to be an obstacle to the participation in and efficiency of PES policies. This study aims to understand transactions related to previous forest plantation programmes and to estimate the actual TCs incurred by farmers who participated in these programmes in a mountainous area of northwestern Vietnam. In addition, this study examines determinants of households’ TCs to test the hypothesis of whether the amount of TCs varies according to household characteristics. Results show that average TCs are not likely to be a constraint for participation since they are about 200,000 VND (USD 10) per household per contract, which is equivalent to one person’s average earnings for about two days of labour. However, TCs amount to more than one-third of the programmes’ benefits, which is relatively high compared to PES programmes in developed countries. This implies that rather than aiming to reduce TCs, an appropriate agenda for policy improvement is to balance the level of TCs with PES programme benefits to enhance the overall attractiveness of afforestation programmes for smallholder farmers. Regression analysis reveals that education, gender and perception towards PES programmes have significant effects on the magnitude of TCs. The analyses also points out the importance of local conditions on the level of TCs, with some unexpected results.