Two-particle entanglement as a property of three-particle entangled states

In a recent article [Phys. Rev. A 54, 1793 (1996)] Krenn and Zeilinger investigated the conditional two-particle correlations for the subensemble of data obtained by selecting the results of the spin measurements by two observers 1 and 2 with respect to the result found in the corresponding measurement by a third observer. In this paper we write out explicitly the condition required in order for the selected results of observers 1 and 2 to violate Bell's inequality for general measurement directions. It is shown that there are infinitely many sets of directions giving the maximum level of violation. Further, we extend the analysis by the authors to the class of triorthogonal states |Psi> = c_1 |z_1>|z_2>|z_3> + c_2 |-z_1>|-z_2>|-z_3>. It is found that a maximal violation of Bell's inequality occurs provided the corresponding three-particle state yields a direct ("all or nothing") nonlocality contradiction.Comment: REVTeX, 7 pages, no figure

Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons

We present a new method for decomposing a 3D voxel shape into disjoint segments using the shape’s simplified surface-skeleton. The surface skeleton of a shape consists of 2D manifolds inside its volume. Each skeleton point has a maximally inscribed ball that touches the boundary in at least two contact points. A key observation is that the boundaries of the simplified fore- and background skeletons map one-to-one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable properties. Our method segments both noisy shapes and shapes with soft edges which vanish over low-curvature regions. Multiscale segmentations can be obtained by varying the simplification level of the skeleton. We present a voxel-based implementation of our approach and illustrate it on several realistic examples.

Geometric Approach to Digital Quantum Information

We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization technique inherently describes a class of pi/2 rotations that connect neighboring states in the set, i.e. that leave the geometrical figures invariant. These rotations are shown to generate the Clifford group, a general group of discrete transformations on N qubits. Discretizing the N-qubit Hilbert space allows us to define its digital quantum information content, and we show that this information content grows as N^2. While we believe the discrete sets are interesting because they allow extra-classical behavior--such as quantum entanglement and quantum parallelism--to be explored while circumventing the continuity of Hilbert space, we also show how they may be a useful tool for problems in traditional quantum computation. We describe in detail the discrete sets for one and two qubits.Comment: Introduction rewritten; 'Sample Application' section added. To appear in J. of Quantum Information Processin

Electron localization : band-by-band decomposition, and application to oxides

Using a plane wave pseudopotential approach to density functional theory we investigate the electron localization length in various oxides. For this purpose, we first set up a theory of the band-by-band decomposition of this quantity, more complex than the decomposition of the spontaneous polarization (a related concept), because of the interband coupling. We show its interpretation in terms of Wannier functions and clarify the effect of the pseudopotential approximation. We treat the case of different oxides: BaO, $\alpha$-PbO, BaTiO$_3$ and PbTiO$_3$. We also investigate the variation of the localization tensor during the ferroelectric phase transitions of BaTiO$_3$ as well as its relationship with the Born effective charges

Enhanced tracking and recognition of moving objects by reasoning about spatio-temporal continuity.

A framework for the logical and statistical analysis and annotation of dynamic scenes containing occlusion and other uncertainties is presented. This framework consists of three elements; an object tracker module, an object recognition/classification module and a logical consistency, ambiguity and error reasoning engine. The principle behind the object tracker and object recognition modules is to reduce error by increasing ambiguity (by merging objects in close proximity and presenting multiple hypotheses). The reasoning engine deals with error, ambiguity and occlusion in a unified framework to produce a hypothesis that satisfies fundamental constraints on the spatio-temporal continuity of objects. Our algorithm finds a globally consistent model of an extended video sequence that is maximally supported by a voting function based on the output of a statistical classifier. The system results in an annotation that is significantly more accurate than what would be obtained by frame-by-frame evaluation of the classifier output. The framework has been implemented and applied successfully to the analysis of team sports with a single camera. Key words: Visua

Affine Subspace Representation for Feature Description

This paper proposes a novel Affine Subspace Representation (ASR) descriptor to deal with affine distortions induced by viewpoint changes. Unlike the traditional local descriptors such as SIFT, ASR inherently encodes local information of multi-view patches, making it robust to affine distortions while maintaining a high discriminative ability. To this end, PCA is used to represent affine-warped patches as PCA-patch vectors for its compactness and efficiency. Then according to the subspace assumption, which implies that the PCA-patch vectors of various affine-warped patches of the same keypoint can be represented by a low-dimensional linear subspace, the ASR descriptor is obtained by using a simple subspace-to-point mapping. Such a linear subspace representation could accurately capture the underlying information of a keypoint (local structure) under multiple views without sacrificing its distinctiveness. To accelerate the computation of ASR descriptor, a fast approximate algorithm is proposed by moving the most computational part (ie, warp patch under various affine transformations) to an offline training stage. Experimental results show that ASR is not only better than the state-of-the-art descriptors under various image transformations, but also performs well without a dedicated affine invariant detector when dealing with viewpoint changes.Comment: To Appear in the 2014 European Conference on Computer Visio