Geometry of qudits

Die vorliegende Diplomarbeit beschäftigt sich überwiegend mit Quanten-Systemen, die zwei (auch qubit genannt) oder im allgemeinsten Fall d Freiheitsgrade (auch qudit genannt) aufweisen. Insbesondere werden die Eigenschaften zusammengesetzter Quanten-Systeme bezüglich Separabilität beziehungsweise Verschränkung auf geometrische Weise dargestellt. Beruhend auf ähnlichen, bereits bekannten Überlegungen für zwei Qubit oder zwei Qudit Systeme, werden mögliche Verallgemeinerungen dieser Ergebnisse für Vielteilchensysteme präsentiert. Des Weiteren wird das Verhalten dieser Vielteilchensysteme bezüglich der gängigsten Separabilit ätskriterien, wie z.B. des Peres-Horodecki Kriteriums, des Realignment Kriteriums, der Destillation von Verschränkung und Verschränkungsmaßen, sowohl numerisch als auch analytisch betrachtet. Es wird im Einzelnen gezeigt wie, in Anlehnung an den zwei Qubit Simplex, ein n-Teilchen Simplex bestehend aus Qubit Zuständen konstruiert werden kann und warum alle Zustände in diesem Simplex 'bound-entangled' sind. Dieses Ergebnis wurde bereits in Physical Review A 78, 042327 (2008) publiziert. Außerdem werden zwei verschiedene Konstruktionen eines n-Teilchen Wk-Simplex vorgestellt, die beide für den n = 2 Fall mit dem bekannten 'Magic Tetrahedron' übereinstimmen. Für den speziellen Fall des drei Teilchen Wk-Simplex (W-Zustand Simplex) werden bestimmte Symmetrien der jeweiligen Quanten Systeme bezüglich der oben erwähnten Separabilitätskriterien aufgezeigt und dementsprechend verschiedene Subklassen von Zustände eingeführt. Zusätzlich zu diesen Symmetrien können durch diese geometrische Veranschaulichung der Zustände, d.h. durch verschiedene Schnitte dieser Simplices, die verschiedenen Kriterien präzise und leicht auf optischem Wege verglichen werden. Aus diesem Grund werden die in dieser Arbeit beschriebenen Ergebnisse dazu beitragen sowohl zusammengesetzte Quanten-Systeme als auch das damit verbundene faszinierende Phänomen der Verschr änkung, welches die Grundlage für zukünftige Technologien, wie etwa Quantenkryptography, Quantenkommunikation oder möglicherweise Quantencomputer, bilden wird, besser zu verstehen.In this thesis, quantum states of two level systems (called qubits) as well as d-level systems (called qudits), d < 1, are investigated. The focus is on characterizing the property of separability and entanglement of composite systems geometrically. Since to some extend this has already been investigated for two qubit or two qudits, this work presents possible generalizations for systems comprising more particles (multipartite). It also shows analytically and numerically how these generalizations affect the prevalent separability criteria such as the Peres-Horodecki criterion, the realignment criterion, the distillation of entanglement and entanglement measures. It is shown in detail how a simplex of n-partite qubit states can be constructed in the similar manner to the bipartite qubit case and why all its elements are bound entangled states. This result is published in Physical Review A 78, 042327 (2008). Furthermore, two different constructions of an n-partite Wk-simplex are presented, which both coincide for n = 2 with the famous magic tetrahedron. For the special cases of the tripartite Wk-simplices (W-state simplices) special symmetries of the eligible quantum systems according to the mentioned separability criteria are revealed and certain subclasses of states can be discriminated. In addition to unveiling these symmetries via this geometrical representation of quantum states, the different cuts of such simplices also allow a precise comparison of the different criteria in a visual and easy way. These facts are therefore contributing to understand and characterize composite quantum systems as well as the associated exciting phenomenon of entanglement and its future applications, such as quantum cryptography, quantum communication or a possible quantum computer

On credibility improvements for automotive navigation systems

Automotive navigation systems are becoming ubiquitous as driver assistance systems. Vendors continuously aim to enhance route guidance by adding new features to their systems. However, we found in an analysis of current navigation systems that many share interaction weaknesses, which can damage the system’s credibility. Such issues are most prevalent when selecting a route, deviating from the route intentionally, or when systems react to dynamic traffic warnings. In this work, we analyze the impact on credibility and propose improved interaction mechanisms to enhance perceived credibility of navigation systems. We improve route selection and the integration of dynamic traffic warnings by optimizing route comparability with relevance-based information display. Further, we show how bidirectional communication between driver and device can be enhanced to achieve a better mapping between device behavior and driver intention. We evaluated the proposed mechanisms in a comparative user study and present results that confirm positive effects on perceived credibility

Teaching Vehicles to Anticipate: A Systematic Study on Probabilistic Behavior Prediction Using Large Data Sets

By observing their environment as well as other traffic participants, humans are enabled to drive road vehicles safely. Vehicle passengers, however, perceive a notable difference between non-experienced and experienced drivers. In particular, they may get the impression that the latter ones anticipate what will happen in the next few moments and consider these foresights in their driving behavior. To make the driving style of automated vehicles comparable to the one of human drivers with respect to comfort and perceived safety, the aforementioned anticipation skills need to become a built-in feature of self-driving vehicles. This article provides a systematic comparison of methods and strategies to generate this intention for self-driving cars using machine learning techniques. To implement and test these algorithms we use a large data set collected over more than 30000 km of highway driving and containing approximately 40000 real-world driving situations. We further show that it is possible to classify driving maneuvers upcoming within the next 5 s with an Area Under the ROC Curve (AUC) above 0.92 for all defined maneuver classes. This enables us to predict the lateral position with a prediction horizon of 5 s with a median lateral error of less than 0.21 m.Comment: the paper has been accepted for publication in IEEE Transcations on Intelligent Transportation Systems (T-ITS) 16 pages 13 figures 12 table

Interaction Weaknesses of Personal Navigation Devices

Automotive navigation systems, especially portable navigation devices (PNDs), are gaining popularity worldwide. Drivers increasingly rely on these devices to guide them to their destination. Some follow them almost blindly, with devastating consequences if the routing goes wrong. Wrong messages as well as superfuous and unnecessary messages can potentially reduce the credibility of those devices. We performed a comparative study with current PNDs from different vendors and market segments, in order to assess the extent of this problem and how it is related to the interaction between device and driver. In this paper, we report the corresponding results and identify multiple interaction weaknesses that are prevalent throughout all tested device classes

Towards Incorporating Contextual Knowledge into the Prediction of Driving Behavior

Predicting the behavior of surrounding traffic participants is crucial for advanced driver assistance systems and autonomous driving. Most researchers however do not consider contextual knowledge when predicting vehicle motion. Extending former studies, we investigate how predictions are affected by external conditions. To do so, we categorize different kinds of contextual information and provide a carefully chosen definition as well as examples for external conditions. More precisely, we investigate how a state-of-the-art approach for lateral motion prediction is influenced by one selected external condition, namely the traffic density. Our investigations demonstrate that this kind of information is highly relevant in order to improve the performance of prediction algorithms. Therefore, this study constitutes the first step towards the integration of such information into automated vehicles. Moreover, our motion prediction approach is evaluated based on the public highD data set showing a maneuver prediction performance with areas under the ROC curve above 97% and a median lateral prediction error of only 0.18m on a prediction horizon of 5s.Comment: the article has been accepted for publication during the 23rd IEEE Intelligent Transportation Systems Conference (ITSC), 7 pages, 6 figures, 1 tabl

CPD: Crowd-based Pothole Detection

Potholes and other damages of the road surface constitute a problem being as old as roads are. Still, potholes are widespread and affect the driving comfort of passengers as well as road safety. If one knew about the exact locations of potholes, it would be possible to repair them selectively or at least to warn drivers about them up to their repair. However, both scenarios require their detection and localization. For this purpose, we propose a crowd-based approach that enables as many of the vehicles already driving on our roads as possible to detect potholes and report them to a centralized back-end application. Whereas each single vehicle provides only limited and imprecise information, it is possible to determine these information more precisely when collecting them at a large scale. These more exact information may, for example, be used to warn following vehicles about potholes lying ahead to increase overall safety and comfort. In this work, this idea is examined and an offline executable version of the desired system is implemented. Additionally, the approach is evaluated with a large database of real-world sensor readings from a testing fleet and therefore its feasibility is proved. Our investigation shows that the suggested CPD approach is promising to bring customers a benefit by an improved driving comfort and higher road safety

A Fleet Learning Architecture for Enhanced Behavior Predictions during Challenging External Conditions

Already today, driver assistance systems help to make daily traffic more comfortable and safer. However, there are still situations that are quite rare but are hard to handle at the same time. In order to cope with these situations and to bridge the gap towards fully automated driving, it becomes necessary to not only collect enormous amounts of data but rather the right ones. This data can be used to develop and validate the systems through machine learning and simulation pipelines. Along this line this paper presents a fleet learning-based architecture that enables continuous improvements of systems predicting the movement of surrounding traffic participants. Moreover, the presented architecture is applied to a testing vehicle in order to prove the fundamental feasibility of the system. Finally, it is shown that the system collects meaningful data which are helpful to improve the underlying prediction systems.Comment: the article has been accepted for publication during the 2020 IEEE Symposium Series on Computational Intelligence (SSCI) within the IEEE Symposium on Computational Intelligence in Vehicles and Transportation Systems (CIVTS), 7 pages, 6 figure

Predicting the Time Until a Vehicle Changes the Lane Using LSTM-based Recurrent Neural Networks

To plan safe and comfortable trajectories for automated vehicles on highways, accurate predictions of traffic situations are needed. So far, a lot of research effort has been spent on detecting lane change maneuvers rather than on estimating the point in time a lane change actually happens. In practice, however, this temporal information might be even more useful. This paper deals with the development of a system that accurately predicts the time to the next lane change of surrounding vehicles on highways using long short-term memory-based recurrent neural networks. An extensive evaluation based on a large real-world data set shows that our approach is able to make reliable predictions, even in the most challenging situations, with a root mean squared error around 0.7 seconds. Already 3.5 seconds prior to lane changes the predictions become highly accurate, showing a median error of less than 0.25 seconds. In summary, this article forms a fundamental step towards downstreamed highly accurate position predictions.Comment: the article has been accepted for publication in IEEE Robotics and Automation Letters (RA-L); the article has been submitted to RA-L with IEEE ICRA conference option; if the article will be presented during the conference will be decided independently; 8 pages, 5 figures, 6 table

Entanglement generation and routing in optical networks

New telecom wavelength sources of polarization entangled photon pairs allow the distribution of entanglement through metro-access networks using standard equipment. This is essential to ease the deployment of future applications that can profit from quantum entanglement, such as quantum cryptography