This report presents a first attempt to introduce noise into the protocol of reference-frame- independent quantum key distribution. It is found that a frequently accepted manner to introduce noise,...Show moreThis report presents a first attempt to introduce noise into the protocol of reference-frame- independent quantum key distribution. It is found that a frequently accepted manner to introduce noise, according to the model of Eckert et al. proposed in ref. [1] leads to non-physical state matrices and therefore another model is proposed: the $\beta_{\pi}$-noise model. In this model the basis states composing the state matrix are perturbed by a complex quantity. For pure states this approach is applied to all state matrix elements, whereas for mixed states it is applied only to the diagonal elements. The off-diagonal elements in the mixed state are perturbed by a complex quantity that is independent of the perturbations on the basis states that the matrix element consists of. Using a Monte Carlo simulation, statistics on the quantum bit error rate as well as the transverse correlation factor are obtained for this model. However, although the $\beta_{\pi}$-noise model solves the main issues that lead to the conclusion that the model of Eckert et al. might infer non-physical state matrices, it does not yet guarantee the state matrix is always physical: a mixed state may still violate positive semi-definiteness. Therefore the original model is improved by perturbing all basis states as before and using this approach for all state matrix elements. In this improved version of the $\beta_{\pi}$-noise model Eve is present as a (complex) scaling of the off-diagonal state matrix elements. Thus, positive semi-definiteness is guaranteed for this noise model. Also for this improved version of the model statistics on the quantum bit error rate and the transverse correlation factor are presented, thereby describing the implications on an experiment.Show less
In this proposal an experiment is envisioned that is principally able to determine whether there exists a fundamental transition between quantum mechanics (QM) and classical mechanics (CM). In the...Show moreIn this proposal an experiment is envisioned that is principally able to determine whether there exists a fundamental transition between quantum mechanics (QM) and classical mechanics (CM). In the quantum realm spatial superpositions of a particle may exist, whereas these superpositions are not observed in the classical world. Many theories have been put forward to explain this difference. Of these, decoherence theories state that there is no explicit difference between QM and CM, but that quantum phenomena are extinguished upon increasing the coupling of the studied object to its environment. Other theories, however, predict that there is a fundamental scale - apart from the environmental coupling - at which spontaneous collapse of a superposition occurs. To test whether such a scale exists, it is proposed to build an interferometer that has a tuneable, coherent amplifier in each of its two arms. The interferometer is fed by a microwave single photon source that yields an entangled superposition of zero and one photon in the arms. The advantage of using microwave photons in a transmission line is that these are carried by electrons, which have a rest mass. Therefore, spontaneous collapse may be expected upon amplifying the superposition of the single photon to such an extent, that the QM-CM transition scale is exceeded. This set-up circumvents the limitation of contemporary experiments that study superpositions of objects fixed in size. By tuning the amplifiers one is now able to smoothly vary the size of the superposition, so that studying the transition scale and its nature becomes experimentally feasible. After introducing the theoretical ideas and the experimental status of the topic, this proposal elaborates on the research goal of the proposed experiment. Then, the method is presented including the experiment's preliminary design options and considerations as well as research steps and risks. Furthermore, the proposal includes a four-year plan of work, discusses the facilities and resources of the host group and stresses collaborations with both theorists and experimentalists.Show less
During this study, a device was developed which is capable of measuring the friction coefficient between two macroscopic solid samples for different rotation angles. It is based on an Anton Paar...Show moreDuring this study, a device was developed which is capable of measuring the friction coefficient between two macroscopic solid samples for different rotation angles. It is based on an Anton Paar rheometer. It can measure torques ranging from 10 nNm up to 200 mNm, while controlling the rotation angle with a minimum resolution of 10 nrad. The normal load exerted on the samples can be controlled with mN accuracy. Measurements on HOPG and silicon dioxide have verified that the instrument works and is capable of measuring very low friction coefficients as a function of the rotation angle between the two samples. The obtained friction coefficients are in agreement with values found in literature.Show less
The Low energy effective Lagrangian of a supersymmetric variation of a Yang--Mills--Higgs Lagrangian, will be derived, where both Lagrangians are still N=2 supersymmetric massless Lagrangians. The...Show moreThe Low energy effective Lagrangian of a supersymmetric variation of a Yang--Mills--Higgs Lagrangian, will be derived, where both Lagrangians are still N=2 supersymmetric massless Lagrangians. The effective Lagrangian is the fixed in a couple of steps in an indirect way. First quantum field theoretic perturbation theory is used for asymptotic behaviour near some identified singularities. Then, with the use of a family of cubic curves as manifolds, and some complex analysis on holomorphic functions, the effective Lagrangian is fixed.Show less
Often low copy number plasmids in bacterial cells exhibit active mechanisms to ensure stable inheritance. In this master thesis we investigate several models that aim to explain the equidistant...Show moreOften low copy number plasmids in bacterial cells exhibit active mechanisms to ensure stable inheritance. In this master thesis we investigate several models that aim to explain the equidistant positioning of pB171 plasmids in E. coli. In this system a walker type ATPase, ParA, forms filamentous structures on the nucleoid. Plasmids with attached ParB, a DNA binding protein, follow the retractive movement of ParA. We show that a polymer pulling model in which the plasmid detachment rate depends critically on the plasmid bound ParB levels can generate partitioning. Furthermore a recently proposed biased diffusion model in which the plasmid diffusion is influenced by the dynamic ParA concentration can direct motion towards mid cell. However the necessity of a high plasmid diffusion constant renders it unlikely to be the actual mechanism used by bacteria. A slight variation of this idea where diffusing oligomers pull on plasmids encounters the same problems as a biased diffusion model. The influence of polymer drag which depends on the length of the filament can be beneficial though it seems unlikely to be the sole mechanism to partition plasmids. Finally, in our favoured model we show that ParA polymers can position plasmids equidistantly with the assumption that ParA subunits bind along the filament and slide to the tip end, thereby influencing the polymerization rate critically.Show less
