10,244 research outputs found
Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem
Although symmetric informationally complete positive operator valued measures
(SIC POVMs, or SICs for short) have been constructed in every dimension up to
67, a general existence proof remains elusive. The purpose of this paper is to
show that the SIC existence problem is equivalent to three other, on the face
of it quite different problems. Although it is still not clear whether these
reformulations of the problem will make it more tractable, we believe that the
fact that SICs have these connections to other areas of mathematics is of some
intrinsic interest. Specifically, we reformulate the SIC problem in terms of
(1) Lie groups, (2) Lie algebras and (3) Jordan algebras (the second result
being a greatly strengthened version of one previously obtained by Appleby,
Flammia and Fuchs). The connection between these three reformulations is
non-trivial: It is not easy to demonstrate their equivalence directly, without
appealing to their common equivalence to SIC existence. In the course of our
analysis we obtain a number of other results which may be of some independent
interest.Comment: 36 pages, to appear in Quantum Inf. Compu
Scene Graph Generation by Iterative Message Passing
Understanding a visual scene goes beyond recognizing individual objects in
isolation. Relationships between objects also constitute rich semantic
information about the scene. In this work, we explicitly model the objects and
their relationships using scene graphs, a visually-grounded graphical structure
of an image. We propose a novel end-to-end model that generates such structured
scene representation from an input image. The model solves the scene graph
inference problem using standard RNNs and learns to iteratively improves its
predictions via message passing. Our joint inference model can take advantage
of contextual cues to make better predictions on objects and their
relationships. The experiments show that our model significantly outperforms
previous methods for generating scene graphs using Visual Genome dataset and
inferring support relations with NYU Depth v2 dataset.Comment: CVPR 201
Doubly infinite separation of quantum information and communication
We prove the existence of (one-way) communication tasks with a subconstant
versus superconstant asymptotic gap, which we call "doubly infinite," between
their quantum information and communication complexities. We do so by studying
the exclusion game [C. Perry et al., Phys. Rev. Lett. 115, 030504 (2015)] for
which there exist instances where the quantum information complexity tends to
zero as the size of the input increases. By showing that the quantum
communication complexity of these games scales at least logarithmically in ,
we obtain our result. We further show that the established lower bounds and
gaps still hold even if we allow a small probability of error. However in this
case, the -qubit quantum message of the zero-error strategy can be
compressed polynomially.Comment: 16 pages, 2 figures. v4: minor errors fixed; close to published
version; v5: financial support info adde
Alternative Measures of State UI Systems
Comparisons among state unemployment insurance (UI) systems can be misleading. Frequently quoted indicators of benefit generosity, tax cost, and adherence to the experience-rating principle are influenced by the relative economic conditions of states. Such comparisons thereby obscure underlying structural differences in state UI systems. A business considering alternative states in which to locate a production facility should be cautious when interpreting UI information in an economic developer's marketing pitch. This paper offers alternative indicators based on how representative firms, with a well specified unemployment experience, would fare in different states. The authors use a micro-simulation approach to model the experiences of representative workers and firms to compare 28 states and contrast the results with those obtained from more conventional indicators. In closing, the authors consider whether a business location decision would be influenced differently by the alternative measures of state UI systems.unemployment, insurance, state, O'Leary, Tannenwald
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