Another convex combination of product states for the separable Werner state

In this paper, we write down the separable Werner state in a two-qubit system explicitly as a convex combination of product states, which is different from the convex combination obtained by Wootters' method. The Werner state in a two-qubit system has a single real parameter and varies from inseparable state to separable state according to the value of its parameter. We derive a hidden variable model that is induced by our decomposed form for the separable Werner state. From our explicit form of the convex combination of product states, we understand the following: The critical point of the parameter for separability of the Werner state comes from positivity of local density operators of the qubits.Comment: 7 pages, Latex2e; v2: 9 pages, title changed, an appendix and a reference added, minor correction

Robust visual odometry using uncertainty models

In dense, urban environments, GPS by itself cannot be relied on to provide accurate positioning information. Signal reception issues (e.g. occlusion, multi-path effects) often prevent the GPS receiver from getting a positional lock, causing holes in the absolute positioning data. In order to keep assisting the driver, other sensors are required to track the vehicle motion during these periods of GPS disturbance. In this paper, we propose a novel method to use a single on-board consumer-grade camera to estimate the relative vehicle motion. The method is based on the tracking of ground plane features, taking into account the uncertainty on their backprojection as well as the uncertainty on the vehicle motion. A Hough-like parameter space vote is employed to extract motion parameters from the uncertainty models. The method is easy to calibrate and designed to be robust to outliers and bad feature quality. Preliminary testing shows good accuracy and reliability, with a positional estimate within 2 metres for a 400 metre elapsed distance. The effects of inaccurate calibration are examined using artificial datasets, suggesting a self-calibrating system may be possible in future work

Perturbative dynamics of fuzzy spheres at large N

We clarify some peculiar aspects of the perturbative expansion around a classical fuzzy-sphere solution in matrix models with a cubic term. While the effective action in the large-N limit is saturated at the one-loop level, we find that the ``one-loop dominance'' does not hold for generic observables due to one-particle reducible diagrams. However, we may exploit the one-loop dominance for the effective action and obtain various observables to all orders from one-loop calculation by simply shifting the center of expansion to the ``quantum solution'', which extremizes the effective action. We confirm the validity of this method by comparison with the direct two-loop calculation and with Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. From the all order result we find that the perturbative expansion has a finite radius of convergence.Comment: 21 pages, 9 figures, (v2) all order analyses added, (v3) some typos correcte

In Darwin’s Garden: an evolutionary exploration of augmented reality in practice

This book is part of the Springer Advanced Information and Knowledge Processing Series and will be published under Springer's Open Access policy.This chapter discusses the rapid developments in augmented reality and mixed reality technologies, from a practitioner’s perspective of making the augmented reality sculptural work In Darwin’s Garden. From its conception in 2012, to its exhibition at Carbon Meets Silicon II in 2017, the advances in augmented reality technology led to an interplay between the goal of the creators and the technological realisation of that vision. The art, design and technology involved, generated a reactive process that was mired in external influences as the accessibility to augmented reality became commercially valuable and subsequently restricted. This chapter will be of interest to anyone who wants to understand more about the possibilities, technologies and processes involved in realising mixed reality practice and about the commercial culture that supports it