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.

Heat stress response for physiological traits in dairy and dual purpose cattle populations on phenotypic and genetic scales

The main objective of this thesis was to determine the potential impact of heat stress (HS) on physiological traits of lactating cows and semen quality of bulls kept in a temperate climate. The thesis is comprised of three studies. An innovative statistical modeling aspect common to all three studies was the application of random regression methodology (RRM) to study the phenotypic and genetic trajectory of traits in dependency of a continuous temperature humidity index (THI). In the first study, semen quality and quantity traits of 562 Holstein sires kept on an AI station in northwestern Germany were analyzed in the course of THI calculated from data obtained from the nearest weather station. Heat stress was identified based on a decline in semen quality and quantity parameters. The identified general HS threshold (THI = 60) and the thermoneutal zone (THI in the range from 50 to 60) for semen production were lower than detected in studies conducted in tropical and subtropical climates. Even though adult bulls were characterized by higher semen productivity compared to younger bulls, they responded with a stronger semen production loss during harsh environments. Heritabilities (low to moderate range) and additive genetic variances of semen characteristics varied with different levels of THI. Also, based on genetic correlations genotype, by environment interactions were detected. Taken together, these findings suggest the application of specific selection strategies for specific climate conditions. In the second study, the effect of the continuous environmental descriptor THI as measured inside the barns on rectal temperatures (RT), skin temperatures (ST), vaginal temperatures (VT), respiration rates (RR), and pulse rate (PR) of lactating Holstein Friesian (HF) and dual-purpose German black pied cattle (DSN) was analyzed. Increasing HS from THI 65 (threshold) to THI 86 (maximal THI) resulted in an increase of RT by 0.6 °C (DSN) and 1 °C (HF), ST by 3.5 °C (HF) and 8 °C (DSN), VT by 0.3 °C (DSN), and RR by 47 breaths / minute (DSN), and decreased PR by 7 beats / minute (DSN). The undesired effects of rising THI on physiological traits were most pronounced for cows with high levels of milk yield and milk constituents, cows in early days in milk and later parities, and during summer seasons in the year 2014. In the third study of this dissertation, the genetic components of the cow’s physiological responses to HS were investigated. Heat stress was deduced from indoor THI measurements, and physiological traits were recorded on native DSN cows and their genetically upgraded crosses with Holstein Friesian sires in two experimental herds from pasture-based production systems reflecting a harsh environment of the northern part of Germany. Although heritabilities were in a low range (from 0.018 to 0.072), alterations of heritabilities, repeatabilities, and genetic components in the course of THI justify the implementation of genetic evaluations including heat stress components. However, low repeatabilities indicate the necessity of using repeated records for measuring physiological traits in German cattle. Moderate EBV correlations between different trait combinations indicate the potential of selection for one trait to simultaneously improve the other physiological attributes. In conclusion, bulls of AI centers and lactating cows suffer from HS during more extreme weather conditions also in the temperate climate of Northern Germany. Monitoring physiological traits during warm and humid conditions could provide precious information for detection of appropriate times for implementation of cooling systems and changes in feeding and management strategies. Subsequently, the inclusion of these physiological traits with THI specific breeding values into overall breeding goals could contribute to improving cattle adaptability by selecting the optimal animal for extreme hot and humid conditions. Furthermore, the recording of meteorological data in close distance to the cow and visualizing the surface body temperature by infrared thermography techniques might be helpful for recognizing heat tolerance and adaptability in cattle.