Mutually unbiased bases in dimension six: The four most distant bases

We consider the average distance between four bases in dimension six. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in dimension six. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically-found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases.Comment: 10 pages, 2 figures, 1 tabl

The Downside Risk of Elevation

Being granted a title enhances the status of the awardee while its loss has an opposite effect. The present article examines whether the latter effect dominates the former in the sense that elevation is less status-enhancing than relegation is status-damaging. Thereto, we use the three consecutive rounds of the German Excellence Initiative (a publicly funded program to promote outstanding research at German universities) as a natural experiment. We provide evidence that the loss of the title as a so-called elite university had a negative effect on the number of first year students. In contrast, we find no evidence for a positive effect on the number of first year students when a university is granted the title

Does distance matter? Tuition Fees and Enrollment of First-Year Students at German Public Universities

We use the recent introduction of tuition fees at public universities in seven of the sixteen German states to identify the effects of tuition fees on university enrollment of first-year students at German public universities. Our study differs from previous research in two important ways. Firstly, we take into account the location of universities and include a spatial variable, which measures the distance between a fee-imposing university and the nearest fee-free alternative. Secondly, we use panel data that allows us to control for unobserved heterogeneity between universities. Our results suggest that enrollment at universities that impose a tuition fee and that are located close to fee-free universities experience a decrease in enrollment that is twice as large as the decrease at universities that are further away from fee-free universities. We also find gender differences in enrollment behavior. Enrollment numbers of female students at universities that are located far away from fee-free alternatives are significantly less affected by the introduction of tuition fees than are enrollment numbers of male students

Does Distance Matter? Tuition Fees and Enrollment of First-Year Students at German Public Universities

We use the recent introduction of tuition fees at public universities in seven of the sixteen German states to identify the effects of tuition fees on university enrollment of first-year students at German public universities. Our study differs from previous research in two important ways. Firstly, we take into account the location of universities and include a spatial variable, which measures the distance between a fee-imposing university and the nearest fee-free alternative. Secondly, we use panel data that allows us to control for unobserved heterogeneity between universities. Our results suggest that enrollment at universities that impose a tuition fee and that are located close to fee-free universities experience a decrease in enrollment that is twice as large as the decrease at universities that are further away from fee-free universities. We also find gender differences in enrollment behavior. Enrollment numbers of female students at universities that are located far away from fee-free alternatives are significantly less affected by the introduction of tuition fees than are enrollment numbers of male students

Alkali suppression within laser ion-source cavities and time structure of the laser ionized ion-bunches

The chemical selectivity of the target and ion-source production system is an asset for Radioactive Ion-Beam (RIB) facilities equipped with mass separators. Ionization via laser induced multiple resonant steps Ionization has such selectivity. However, the selectivity of the ISOLDE Resonant Ionization Laser Ion-Source (RILIS), where ionization takes place within high temperature refractory metal cavities, suffers from unwanted surface ionization of low ionization potential alkalis. In order to reduce this type of isobaric contaminant, surface ionization within the target vessel was used. On-line measurements of the efficiency of this method is reported, suppression factors of alkalis up to an order of magnitude were measured as a function of their ionization potential. The time distribution of the ion bunches produced with the RILIS was measured for a variety of elements and high temperature cavity materials. While all ions are produced within a few nanoseconds, the ion bunch sometimes spreads over more than 100 ms. This demonstrates that ions are confined within high temperature metallic cavities. It is the internal electrical field of these cavities that causes the ions to drifts to the extraction region and defines the dwell time of the ions in the cavity. Beam optics calculations were carried out to simulate the pulse shape of a RILIS ion bunch and are compared to the actual measurements

Optimal quantum control in nanostructures: Theory and application to generic three-level system

Coherent carrier control in quantum nanostructures is studied within the framework of Optimal Control. We develop a general solution scheme for the optimization of an external control (e.g., lasers pulses), which allows to channel the system's wavefunction between two given states in its most efficient way; physically motivated constraints, such as limited laser resources or population suppression of certain states, can be accounted for through a general cost functional. Using a generic three-level scheme for the quantum system, we demonstrate the applicability of our approach and identify the pertinent calculation and convergence parameters.Comment: 7 pages; to appear in Phys. Rev.

Tomographic Quantum Cryptography: Equivalence of Quantum and Classical Key Distillation

The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.Comment: 4 pages, 1 figur