Research on curriculum resources in mathematics education: a survey of the field - Rezat, Sebastian (ZDM – Mathematics Education)
Abstract This survey describes the structure of the field of research on curriculum resources in mathematics education in the period from 2018 till 2023. Based on the procedures of a systematic review relevant literature was identified using Web of Science as a database. The included literature was analyzed and categorized according to the type of curriculum resource and the area of study. Seven areas of studies were identified: studies on the role of curriculum resources, content analysis, user studies, studies on the effects of curriculum resources, studies on curriculum resource design, curriculum resources as data, and reviews. The areas were further subdivided into different subcategories based on the research questions of the included papers. The findings show that research on mathematics textbooks is still predominant in the field. The most popular areas of research are content analysis, user studies, studies on design, and studies on effects. Emerging areas are research on students’ use of curriculum resources and the employment of user data from digital curriculum resources as data basis in mathematics education research.

Open Educational Resources und Lehrkräftebildung. Potenziale und Ressourcen. - Weber, Tassja (Lehrkräftebildung in der digitalen Welt. Zukunftsorientierte Forschungs- und Praxisperspektiven)
In einer digital geprägten Welt ist die zukunftsfähige Professionalisierung von (angehenden) Lehrkräften eine der zentralen Aufgaben lehrkräftebildender Hochschulen. Für eine kohärente und abgestimmte Kompetenzentwicklung ist insbesondere die nachhaltige Verankerung von Lern- und Bildungsgelegenheiten in einem fakultätsübergreifend organisierten Lehramtsstudium erfolgversprechend, aber auch herausfordernd. Der Band Lehrkräftebildung in der digitalen Welt – zukunftsorientierte Forschungs- und Praxisperspektiven beschreibt fakultäts- und fächerübergreifende Möglichkeiten im Bereich der Förderung digitaler Kompetenzen in der Lehrkräftebildung. Vorgestellt werden theoretische und empirische Arbeiten, Analysen und Diskussionen zu digitalisierungsbezogenen Forschungsfeldern sowie Initiativen, Praxisberichte und (Lehr-)Konzeptionen. Es handelt sich um den ersten Band der Reihe Paderborner Beiträge zur Bildungsforschung und Lehrkräftebildung, die von der PLAZ – Professional School of Education herausgegeben wird.

The Hochschild cohomology ring of monomial algebras - Artenstein, Dalia; Letz, Janina Carmen; Oswald, Amrei; Solotar, Andrea (J. Algebra)

Music and Religions in the 21st Century

The Topicality and Diversity of a Religious Genre. German Oratorios in the 21st Century - Höink, Dominik (Music and Religions in the 21st Century)

Gesundheitskompetenzen entwickeln – Studierende für das Berufsfeld Schule stärken - Decker, Claudia; Wobbe, Lena

Tax Loss Carryforward Disclosure - Müller, Jens; Flagmeier, Vanessa (Schmalenbach Journal of Business Research)

Using Digital Nudging in Medical decision-making – A Taxonomy to Inform Research and Practice - Hövel, Gilbert Georg; Schütz, Florian; Trang, Simon Thanh-Nam (PACIS 2024 Proceedings)

Will the Ransom Be Paid? Examining Influencing Factors of the Ransomware-Payment Decision - Hövel, Gilbert Georg; Veynshter, Anton; Schütz, Florian; Trang, Simon Thanh-Nam (ECIS 2024 Proceedings)

The Lower the Risk, the Lower the Premium? Conceptualizing an Artifact for Usage-Based Pricing of Personal Cyber Insurance Policies - Schütz, Florian; Lukowitsch, Alexander; Hövel, Gilbert; Trang, Simon (ECIS 2024 Proceedings)

Fortifying the Human Firewall: Designing a Virtual Reality-Based Test to Measure Individuals' Cyber Security Competencies - Schütz, Florian; Steenken, Lennart; Menck, jannes; Hugenberg, Simon; Köpfer, Patricia; Hövel, Gilbert; Trang, Simon (PACIS 2024)

Do Investors Surf the Darknet? Exploring the Impact of Darknet Announcements on Market Reactions - Brinkmeier, Tim; Hövel, Gilbert Georg; Trang, Simon Thanh-Nam

Relative-belief inference in quantum information theory - Teo, Y. S.; Shringarpure, S. U.; Jeong, H.; Prasannan, Nidhin; Brecht, Benjamin; Silberhorn, Christine; Evans, M.; Mogilevtsev, D.; Sánchez-Soto, L. L. (Physical Review A)
We introduce the framework of Bayesian relative belief that directly evaluates whether or not the experimental data at hand support a given hypothesis regarding a quantum system by directly comparing the prior and posterior probabilities for the hypothesis. In model-dimension certification tasks, we show that the relative-belief procedure typically chooses Hilbert spaces that are never smaller in dimension than those selected from optimizing a broad class of information criteria, including Akaike's criterion. As a concrete and focused exposition of this powerful evidence-based technique, we apply the relative-belief procedure to an important application: . In particular, just by comparing prior and posterior probabilities based on data, we demonstrate its capability of tracking multiphoton emissions using (realistically lossy) single-photon detectors in order to assess the actual quality of photon sources without making assumptions, thereby reliably safeguarding source integrity for general quantum-information and communication tasks with Bayesian reasoning. Finally, we discuss how relative belief can be exploited to carry out parametric model certification and estimate the total dimension of the quantum state for the combined (measured) physical and interacting external systems described by the Tavis-Cummings model. Published by the American Physical Society 2024

Pulse characterization at the single-photon level through chronocyclic Q-function measurements - Bhattacharjee, Abhinandan; Folge, Patrick Fabian; Serino, Laura Maria; Řeháček, Jaroslav; Hradil, Zdeněk; Silberhorn, Christine; Brecht, Benjamin (Optics Express)
The characterization of the complex spectral amplitude, that is, the spectrum and spectral phase, of single-photon-level light fields is a crucial capability for modern photonic quantum technologies. Since established pulse characterization techniques are not applicable at low intensities, alternative approaches are required. Here, we demonstrate the retrieval of the complex spectral amplitude of single-photon-level light pulses through measuring their chronocyclic Q −function. Our approach draws inspiration from quantum state tomography by exploiting the analogy between quadrature phase space and time-frequency phase space. In the experiment, we perform time-frequency projections with a quantum pulse gate (QPG), which directly yield the chronocyclic Q −function. We evaluate the complex spectral amplitude from the measured chronocyclic Q −function data with maximum likelihood estimation (MLE), which is the established technique for quantum state tomography. The MLE yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any a priori information, but also allows for, in principle, estimating the spectral-temporal coherence properties of the state. Our method accurately recovers features such as jumps in the spectral phase and is resistant against regions with zero spectral intensity, which makes it immediately beneficial for classical pulse characterization problems.

Evidence-Based Certification of Quantum Dimensions - Teo, Y. S.; Shringarpure, S. U.; Jeong, H.; Prasannan, Nidhin; Brecht, Benjamin; Silberhorn, Christine; Evans, M.; Mogilevtsev, D.; Sánchez-Soto, L. L. (Physical Review Letters)
Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and continuous variables that is fully evidence based, relying solely on the experimental data collected and no other unjustified assumptions whatsoever. Using the Bayesian concept of relative belief, we take the effective dimension of the state as the smallest one such that the posterior probability is larger than the prior, as dictated by the data. The posterior probabilities associated with the relative-belief ratios measure the strength of the evidence provide by these ratios so that we can assess whether there is weak or strong evidence in favor or against a particular dimension. Using experimental data from spectral-temporal and polarimetry measurements, we demonstrate how to correctly assign Bayesian plausible error bars for the obtained effective dimensions. This makes relative belief a conservative and easy-to-use model-selection method for any experiment. Published by the American Physical Society 2024

Realization of high-fidelity unitary operations on up to 64 frequency bins - De, Syamsundar; Ansari, Vahid; Sperling, Jan; Barkhofen, Sonja; Brecht, Benjamin; Silberhorn, Christine (Physical Review Research)
The ability to apply user-chosen large-scale unitary operations with high fidelity to a quantum state is key to realizing future photonic quantum technologies. Here, we realize the implementation of programmable unitary operations on up to 64 frequency-bin modes. To benchmark the performance of our system, we probe different quantum walk unitary operations, in particular, Grover walks on four-dimensional hypercubes with similarities exceeding 95% and quantum walks with 400 steps on circles and finite lines with similarities of 98%. Our results open a path toward implementing high-quality unitary operations, which can form the basis for applications in complex tasks, such as Gaussian boson sampling. Published by the American Physical Society 2024

A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates - Folge, Patrick Fabian; Stefszky, Michael; Brecht, Benjamin; Silberhorn, Christine (PRX Quantum)
Linear optical quantum networks, consisting of a quantum input state and a multiport interferometer, are an important building block for many quantum technological concepts, e.g., Gaussian boson sampling. Here, we propose the implementation of such networks based on frequency conversion by utilizing a so-called multioutput quantum pulse gate (MQPG). This approach allows the resource-efficient and therefore scalable implementation of frequency-bin-based, fully programmable interferometers in a single spatial and polarization mode. Quantum input states for this network can be provided by utilizing the strong frequency entanglement of a type-0 parametric down-conversion (PDC) source. Here, we develop a theoretical framework to describe linear networks based on an MQPG and PDC and utilize it to investigate the limits and scalabilty of our approach. Published by the American Physical Society 2024

Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate - Serino, Laura Maria; Eigner, Christof; Brecht, Benjamin; Silberhorn, Christine (Optics Express)
We demonstrate a high-dimensional mode-sorter for single photons based on a multi-output quantum pulse gate, which we can program to switch between different temporal-mode encodings including pulse modes, frequency bins, time bins, and their superpositions. This device can facilitate practical realizations of quantum information applications such as high-dimensional quantum key distribution and thus enables secure communication with enhanced information capacity. We characterize the mode-sorter through a detector tomography in 3 and 5 dimensions and find a fidelity up to 0.958 ± 0.030 at the single-photon level.

Low-noise balanced homodyne detection with superconducting nanowire single-photon detectors - Protte, Maximilian; Schapeler, Timon; Sperling, Jan; Bartley, Tim (Optica Quantum)
Superconducting nanowire single-photon detectors (SNSPDs) have been widely used to study the discrete nature of quantum states of light in the form of photon-counting experiments. We show that SNSPDs can also be used to study continuous variables of optical quantum states by performing homodyne detection at a bandwidth of 400 kHz. By measuring the interference of a continuous-wave field of a local oscillator with the field of the vacuum state using two SNSPDs, we show that the variance of the difference in count rates is linearly proportional to the photon flux of the local oscillator over almost five orders of magnitude. The resulting shot-noise clearance of (46.0 ± 1.1) dB is the highest reported clearance for a balanced optical homodyne detector, demonstrating their potential for measuring highly squeezed states in the continuous-wave regime. In addition, we measured a CMRR = 22.4 dB. From the joint click counting statistics, we also measure the phase-dependent quadrature of a weak coherent state to demonstrate our device’s functionality as a homodyne detector.

An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition - Biermann, Michael; Leppin, Christian; Langhoff, Arne; Ziemer, Thorben; Rembe, Christian; Johannsmann, Diethelm (The Analyst)
Using a precise electrochemical quartz crystal microbalance (EQCM), it was shown that electrogravimetry can be carried out with microelectrode arrays (MEAs). Significant differences between the potential dependent adsorption of a redox-active molecule and electroplating were presented.