Was man von zwei Qubits über Quantenphysik lernen kann: Verschränkung und Quantenkorrelationen

In diesem Artikel wird der Zugang zur Quantenphysik über das einfachst mögliche Modellsystem, das Qubit, erweitert zu der Kombination von zwei Qubits. Dabei tritt erstmals das für die Quantenphysik zentrale Konzept der Verschränkung auf, welches nicht nur seltsame Eigenschaften der Quantenphysik illustriert, sondern auch der Schlüssel zum Verständnis von modernen Anwendungen der Quantenphysik ist. Ähnlich wie im Falle des einzelnen Qubits wird dabei versucht, die Grundprinzipien von Verschränkung und deren Anwendung mit Hilfe einfacher Mathematik und Bilder zu vermitteln, wobei Visualisierungen eine zentrale Rolle spielen. Die behandelten Themen umfassen verschränkte Zustände, Operationen und Messungen. Die möglichen physikalischen Realisierungen und Anwendungen, insbesondere im Bereich der Quanteninformation, werden hier kurz angesprochen, und in einer weiteren Publikation vertieft diskutiert

Was man von zwei Qubits über Quantenphysik lernen kann: Verschränkung und Quantenkorrelationen

In diesem Artikel wird der Zugang zur Quantenphysik über das einfachst mögliche Modellsystem, das Qubit, erweitert zu der Kombination von zwei Qubits. Dabei tritt erstmals das für die Quantenphysik zentrale Konzept der Verschränkung auf, welches nicht nur seltsame Eigenschaften der Quantenphysik illustriert, sondern auch der Schlüssel zum Verständnis von modernen Anwendungen der Quantenphysik ist. Ähnlich wie im Falle des einzelnen Qubits wird dabei versucht, die Grundprinzipien von Verschränkung und deren Anwendung mit Hilfe einfacher Mathematik und Bilder zu vermitteln, wobei Visualisierungen eine zentrale Rolle spielen. Die behandelten Themen umfassen verschränkte Zustände, Operationen und Messungen. Die möglichen physikalischen Realisierungen und Anwendungen, insbesondere im Bereich der Quanteninformation, werden hier kurz angesprochen, und in einer weiteren Publikation vertieft diskutiert

Accuracy and feasibility of a dedicated image guidance solution for endoscopic lateral skull base surgery.

OBJECTIVE We aimed to design, build and validate a surgical navigation system which fulfills the accuracy requirements for surgical procedures on the ear and the lateral skull base, and which integrates with the endoscopic workflow and operating room setup. MATERIALS AND METHODS The navigation system consists of portable tablet computer (iPad Pro, Apple Computer, USA) and an optical tracking system (Cambar B1, Axios3D, Germany), both connected via a wireless Bluetooth link and attached directly to the OR table. Active optical tracking references are rigidly fixed to both the patient and surgical tools. Software to support image import, registration and 2D/3D visualization has been developed. Two models were used for targeting accuracy assessment: a technical phantom model and an ex vivo temporal bone model. Additionally, workflow integration and usability of the navigation system during endoscopic lateral skull base procedures was investigated in ex vivo experiments on 12 sides of cadaver head specimens. RESULTS The accuracy experiments revealed a target registration error in the technical phantom model of 0.20 ± 0.10 mm (n = 36) and during the ex vivo assessment of 0.28 ± 0.10 mm (n = 21). Navigation was successfully carried out in n = 36 procedures (infracochlear, suprageniculate and transpromontorial approach), with navigated instruments usable without interference with the endoscope. The system aided in the successful and accurate identification of vital anatomical structures. CONCLUSIONS Useful surgical navigation is, to a large extent, a result of sufficiently accurate tracking technology. We have demonstrated sufficient accuracy and a potentially suitable integration for surgical application within endoscopic lateral skull base procedures

Risk Factors Promoting Hypertensive Crises: Evidence From a Longitudinal Study

Background Current knowledge about risk factors promoting hypertensive crisis originates from retrospective data. Therefore, potential risk factors of hypertensive crisis were assessed in a prospective longitudinal study. Methods Eighty-nine patients of the medical outpatient unit at the University Hospital of Bern (Bern, Switzerland) with previously diagnosed hypertension participated in this study. At baseline, 33 potential risk factors were assessed. All patients were followed-up for the outcome of hypertensive crisis. Cox regression models were used to detect relationships between risk factors and hypertensive crisis (defined as acute rise of systolic blood pressure (BP) ≥200mmHg and/or diastolic BP ≥120mmHg). Results The mean duration of follow-up was 1.6 ± 0.3 years (range 1.0-2.4 years). Four patients (4.5%) were lost to follow-up. Thirteen patients (15.3%) experienced hypertensive crisis during follow-up. Several potential risk factors were significantly associated with hypertensive crisis: female sex, higher grades of obesity, the presence of a hypertensive or coronary heart disease, the presence of a somatoform disorder, a higher number of antihypertensive drugs, and nonadherence to medication. As measured by the hazard ratio, nonadherence was the most important factor associated with hypertensive crisis (hazard ratio 5.88, 95% confidence interval 1.59-21.77, P < 0.01). Conclusions This study identified several potential risk factors of hypertensive crisis. Results of this study are consistent with the hypothesis that improvement of medical adherence in antihypertensive therapy would help to prevent hypertensive crises. However, larger studies are needed to assess potential confounding, other risk factors and the possibility of interaction between predictor

Algorithmic copositivity detection by simplicial partition

AbstractWe present new criteria for copositivity of a matrix, i.e., conditions which ensure that the quadratic form induced by the matrix is nonnegative over the nonnegative orthant. These criteria arise from the representation of the quadratic form in barycentric coordinates with respect to the standard simplex and simplicial partitions thereof. We show that, as the partition gets finer and finer, the conditions eventually capture all strictly copositive matrices. We propose an algorithmic implementation which considers several numerical aspects. As an application, we present results on the maximum clique problem. We also briefly discuss extensions of our approach to copositivity with respect to arbitrary polyhedral cones

An improved algorithm to test copositivity

Copositivity plays a role in combinatorial and nonconvex quadratic optimization. However, testing copositivity of a given matrix is a co-NP-complete problem. We improve a previously given branch-and-bound type algorithm for testing copositivity and discuss its behavior in particular for the maximum clique problem. Numerical experiments indicate that the speedup is considerable.