Sequence Of Local Operations Research Articles

Do Neural Networks for Segmentation Understand Insideness?

The insideness problem is an aspect of image segmentation that consists of determining which pixels are inside and outside a region. Deep neural networks (DNNs) excel in segmentation benchmarks, but it is unclear if they have the ability to solve the insideness problem as it requires evaluating long-range spatial dependencies. In this letter, we analyze the insideness problem in isolation, without texture or semantic cues, such that other aspects of segmentation do not interfere in the analysis. We demonstrate that DNNs for segmentation with few units have sufficient complexity to solve the insideness for any curve. Yet such DNNs have severe problems with learning general solutions. Only recurrent networks trained with small images learn solutions that generalize well to almost any curve. Recurrent networks can decompose the evaluation of long-range dependencies into a sequence of local operations, and learning with small images alleviates the common difficulties of training recurrent networks with a large number of unrolling steps.

Strong Quantum Nonlocality without Entanglement.

Quantum nonlocality is usually associated with entangled states by their violations of Bell-type inequalities. However, even unentangled systems, whose parts may have been prepared separately, can show nonlocal properties. In particular, a set of product states is said to exhibit "quantum nonlocality without entanglement" if the states are locally indistinguishable; i.e., it is not possible to optimally distinguish the states by any sequence of local operations and classical communication. Here, we present a stronger manifestation of this kind of nonlocality in multiparty systems through the notion of local irreducibility. A set of multiparty orthogonal quantum states is defined to be locally irreducible if it is not possible to locally eliminate one or more states from the set while preserving orthogonality of the postmeasurement states. Such a set, by definition, is locally indistinguishable, but we show that the converse does not always hold. We provide the first examples of orthogonal product bases on C^{d}⊗C^{d}⊗C^{d} for d=3, 4 that are locally irreducible in all bipartitions, where the construction for d=3 achieves the minimum dimension necessary for such product states to exist. The existence of such product bases implies that local implementation of a multiparty separable measurement may require entangled resources across all bipartitions.

Quantum nonlocality without entanglement

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles that also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.

Free Form Modeling with History

We present a new kind of surface made by a hybrid of parametric mapping and free form deformation. The surface is mapped from an original parametric space, and then subjected to a sequence of deformation operations. Rather than express the deformations with a global grid, they are described as a sequence of local operations. The surface shape is thus defined by the history of operations that formed it. Each of these deformation operations is encapsulated in a structure of control information known as a 'feature'. Features are manipulated by means of reference points on the surface known as handles and by means of widgets that alter their properties. The calculation of the surface from this structure is very efficient and permits interactive display of complex models. The result of this approach is that we have been able to build an interactive modeler for free form surfaces with a remarkably natural feel. The user directly manipulates a block of infinitely stretchable plastic clay. Because the surface is continuously mapped from a parametric space, it is easy to add solid texture. The surface can be further deformed after texturing, maintaining a correspondence between texture and surface features.