Quantum Information Theory of Entanglement and Measurement

We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the description of quantum ensembles. We find that quantum conditional entropies can be negative for entangled systems, which leads to a violation of well-known bounds in Shannon information theory. Such a unified information-theoretic description of classical correlation and quantum entanglement clarifies the link between them: the latter can be viewed as ``super-correlation'' which can induce classical correlation when considering a tripartite or larger system. Furthermore, negative entropy and the associated clarification of entanglement paves the way to a natural information-theoretic description of the measurement process. This model, while unitary and causal, implies the well-known probabilistic results of conventional quantum mechanics. It also results in a simple interpretation of the Kholevo theorem limiting the accessible information in a quantum measurement.Comment: 26 pages with 6 figures. Expanded version of PhysComp'96 contributio

A cognitive exploration of the “non-visual” nature of geometric proofs

Why are Geometric Proofs (Usually) “Non-Visual”? We asked this question as a way to explore the similarities and differences between diagrams and text (visual thinking versus language thinking). Traditional text-based proofs are considered (by many to be) more rigorous than diagrams alone. In this paper we focus on human perceptual-cognitive characteristics that may encourage textual modes for proofs because of the ergonomic affordances of text relative to diagrams. We suggest that visual-spatial perception of physical objects, where an object is perceived with greater acuity through foveal vision rather than peripheral vision, is similar to attention navigating a conceptual visual-spatial structure. We suggest that attention has foveal-like and peripheral-like characteristics and that textual modes appeal to what we refer to here as foveal-focal attention, an extension of prior work in focused attention

Teaching Mathematics with Poetry: Some Activities

During the summer of 2021, I experimented with a new way of getting children excited about mathematics: math poetry. Math can be a trigger word for some children and many adults. I wanted to find a way to make learning math fun—without the students knowing they’re doing math. In this paper I describe some activities I used with students ranging from grades K-12 to the college level and share several poem examples, from students in grades two to eight

License GPL-2 NeedsCompilation No Repository CRAN

Description Various R programming tools for plotting dat

Evidence for Distinct Components of the Galactic Stellar Halo from 838 RR Lyrae Stars Discovered in the LONEOS-I Survey

We present 838 ab-type RR Lyrae stars from the Lowell Observatory Near Earth Objects Survey Phase I (LONEOS-I). These objects cover 1430 deg^2 and span distances ranging from 3-30 kpc from the Galactic Center. Object selection is based on phased, photometric data with 28-50 epochs. We use this large sample to explore the bulk properties of the stellar halo, including the spatial distribution. The period-amplitude distribution of this sample shows that the majority of these RR Lyrae stars resemble Oosterhoff type I, but there is a significant fraction (26 %) which have longer periods and appear to be Oosterhoff type II. We find that the radial distributions of these two populations have significantly different profiles (rho_{OoI} ~ R^(-2.26 +- 0.07) and rho_{OoII} ~ R^(-2.88 +- 0.11). This suggests that the stellar halo was formed by at least two distinct accretion processes and supports dual-halo models.Comment: 18 pages, 28 figures, apjemulated, minor corrections and clarifications. Accepted to ApJ on Jan 21, 200

The Everyday Math Guide: Seeing and Using Math in Your Daily Life

This textbook was created to align with many of the Arkansas standards for the Quantitative Literacy course MATH 1113 in the Arkansas Course Transfer system.https://orc.library.atu.edu/atu_oer/1003/thumbnail.jp