Physical Sciences and Mathematics Commons^™

Weak Values Are Universal In Von Neumann Measurements, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system observable. For any coupling strength, any initial states, and any choice of conditioning, the averages of the detector position and momentum are completely described by the real parts of three generalized weak values in the joint Hilbert space. Higher-order detector moments also have similar weak value expansions. Using the Wigner distribution of the initial detector state, we find compact expressions for …

Efficient High-Dimensional Entanglement Imaging With A Compressive-Sensing Double-Pixel Camera, Gregory A. Howland, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We implement a double-pixel compressive-sensing camera to efficiently characterize, at high resolution, the spatially entangled fields that are produced by spontaneous parametric down-conversion. This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster scanning by a scaling factor up to n²/log(n) for n-dimensional images. We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon. By comparing the entangled photons’ classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions. More broadly, our result indicates that …

Building A Computer Program To Support Children, Parents, And Distraction During Healthcare Procedures, Kirsten Hanrahan, Ann Marie Mccarthy, Charmaine Kleiber, Kaan Ataman, W. Nick Street, M. Bridget Zimmerman, Annel L. Ersig

Business Faculty Articles and Research

This secondary data analysis used data mining methods to develop predictive models of child risk for distress during a healthcare procedure. Data used came from a study that predicted factors associated with children's responses to an intravenous catheter insertion while parents provided distraction coaching. From the 255 items used in the primary study, 44 predictive items were identified through automatic feature selection and used to build support vector machine regression models. Models were validated using multiple cross-validation tests and by comparing variables identified as explanatory in the traditional versus support vector machine regression. Rule-based approaches were applied to the model …

Serpentine Low Loss Trapezoidal Silica Waveguides On Silicon, Xiaomin Zhang, Mark Harrison, Audrey Harker, Andrea M. Armani

Engineering Faculty Articles and Research

We report the fabrication and characterization of straight and serpentine low loss trapezoidal silica waveguides integrated on a silicon substrate. The waveguide channel was defined using a dual photo-lithography and buffered HF etching and isolated from the silicon substrate using an isotropic silicon etchant. The waveguide is air-clad and thus has a core-cladding effective index contrast of approximately 25%. Measured at 658, 980 and 1550nm, the propagation loss was found to be 0.69, 0.59, and 0.41dB/cm respectively, with a critical bending radius less than 375μm. The waveguide’s polarization behavior was investigated both theoretically and experimentally. Additionally, the output power shows …

Double Lorentzian Atomic Prism, David J. Starling, Steven M. Bloch, Praveen K. Vudyasetu, Joseph S. Choi, Bethany Little, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present an atomic prism spectrometer that utilizes the steep linear dispersion between two strongly absorbing hyperfine resonances of rubidium. We resolve spectral lines 50 MHz apart and, utilizing a larger part of the available spectrum than only between the two resonances, we spatially separate collinear pump, signal, and idler beams resulting from a four-wave mixing process. Due to the high transparency possible between the resonances, these results have applications in the filtering of narrow-band entangled photons and interaction-free measurements.

Quantum Mutual Information Capacity For High-Dimensional Entangled States, P. Ben Dixon, Gregory A. Howland, James Schneeloch, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

High-dimensional Hilbert spaces used for quantum communication channels offer the possibility of large data transmission capabilities. We propose a method of characterizing the channel capacity of an entangled photonic state in high-dimensional position and momentum bases. We use this method to measure the channel capacity of a parametric down-conversion state by measuring in up to 576 dimensions per detector. We achieve a channel capacity over 7  bits/photon in either the position or momentum basis. Furthermore, we provide a correspondingly high-dimensional separability bound that suggests that the channel performance cannot be replicated classically.

Contextual-Value Approach To The Generalized Measurement Of Observables, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104, 240401 (2011)]. The theory of contextual values is a principled approach to the generalized measurement of observables. It extends the well-established theory of generalized statemeasurements by bridging the gap between partial state collapse and the observables that represent physically relevant information about the system. To emphasize the general utility of the concept, we first construct the full theory of contextual values within an operational formulation of classical probability theory, paying special attention to observable …

From Velocities To Fluxions, Marco Panza

MPP Published Research

"Though the De Methodis results, for its essential structure and content, from a re-elaboration of a previous unfinished treatise composed in the Fall of 1666—now known, after Whiteside, as The October 1666 tract on fluxions ([22], I, pp. 400-448)—, the introduction of the term ‘fluxion’ goes together with an important conceptual change concerned with Newton’s understanding of his own achievements. I shall argue that this change marks a crucial step in the origins of analysis, conceived as an autonomous mathematical theory."

Significance Of The Imaginary Part Of The Weak Value, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

Unlike the real part of the generalized weak value of an observable, which can in a restricted sense be operationally interpreted as an idealized conditioned average of that observable in the limit of zero measurement disturbance, the imaginary part of the generalized weak value does not provide information pertaining to the observable being measured.What it does provide is direct information about howthe initial statewould be unitarily disturbed by the observable operator. Specifically, we provide an operational interpretation for the imaginary part of the generalized weak value as the logarithmic directional derivative of the postselection probability along the unitary flow generated …

Measuring Which-Path Information With Coupled Electronic Mach-Zehnder Interferometers, Justin Dressel, Y. Choi, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We theoretically investigate a generalized “which-path” measurement on an electronic Mach-Zehnder Interferometer (MZI) implemented via Coulomb coupling to a second electronic MZI acting as a detector. The use of contextual values, or generalized eigenvalues, enables the precise construction of which-path operator averages that are valid for any measurement strength from the available drain currents. The form of the contextual values provides direct physical insight about the measurement being performed, providing information about the correlation strength between system and detector, the measurement inefficiency, and the proper background removal. We find that the detector interferometer must display maximal wavelike behavior to optimally …

Toward A Framework For Systematic Error Modeling Of Spaceborne Precipitation Radar With Noaa/Nssl Ground Radar Based National Mosaic Qpe, Pierre-Emmanuel Kirstetter, Y. Hong, J. J. Gourley, S. Chen, Z. Flamig, J. Zhang, M. Schwaller, W. Peterson, Eyal Amitai

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Characterization of the error associated with satellite rainfall estimates is a necessary component of deterministic and probabilistic frameworks involving spaceborne passive and active microwave measurements for applications ranging from water budget studies to forecasting natural hazards related to extreme rainfall events. The authors focus here on the error structure of NASA's Tropical Rainfall Measurement Mission (TRMM) Precipitation Radar (PR) quantitative precipitation estimation (QPE) at ground. The problem is addressed by comparison of PR QPEs with reference values derived from ground-based measurements using NOAA/NSSL ground radar based National Mosaic and QPE system (NMQ/Q2). A preliminary investigation of this subject has been …

Bicomplex Numbers And Their Elementary Functions, M. E. Luna-Elizarrarás, M. Shapiro, Daniele C. Struppa, Adrian Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we introduce the algebra of bicomplex numbers as a generalization of the field of complex numbers. We describe how to define elementary functions in such an algebra (polynomials, exponential functions, and trigonometric functions) as well as their inverse functions (roots, logarithms, inverse trigonometric functions). Our goal is to show that a function theory on bicomplex numbers is, in some sense, a better generalization of the theory of holomorphic functions of one variable, than the classical theory of holomorphic functions in two complex variables.

Distributed Simulated Annealing With Mapreduce, Atanas Radenski

Mathematics, Physics, and Computer Science Faculty Books and Book Chapters

Simulated annealing’s high computational intensity has stimulated researchers to experiment with various parallel and distributed simulated annealing algorithms for shared memory, message-passing, and hybrid-parallel platforms. MapReduce is an emerging distributed computing framework for large-scale data processing on clusters of commodity servers; to our knowledge, MapReduce has not been used for simulated annealing yet. In this paper, we investigate the applicability of MapReduce to distributed simulated annealing in general, and to the TSP in particular. We (i) design six algorithmic patterns of distributed simulated annealing with MapReduce, (ii) instantiate the patterns into MR implementations to solve a sample TSP problem, and …

Completeness For The Coalgebraic Cover Modality, Clemens Kupke, Alexander Kurz, Yde Venema

Engineering Faculty Articles and Research

We study the finitary version of the coalgebraic logic introduced by L. Moss. The syntax of this logic, which is introduced uniformly with respect to a coalgebraic type functor, required to preserve weak pullbacks, extends that of classical propositional logic with a so-called coalgebraic cover modality depending on the type functor. Its semantics is defined in terms of a categorically defined relation lifting operation.

As the main contributions of our paper we introduce a derivation system, and prove that it provides a sound and complete axiomatization for the collection of coalgebraically valid inequalities. Our soundness and completeness proof is algebraic, …

Entropy And Information Causality In General Probabilistic Theories (Addendum), Howard Barnum, Jonathan Barrett, Lisa Orloff Clark, Matthew S. Leifer, Robert Spekkens, Nicholas Stepanik, Alex Wilce, Robin Wilke

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this addendum to our paper (2010 New J. Phys. 12 033024), we point out that an elementary consequence of the strong subadditivity inequality allows us to strengthen one of the main conclusions of that paper.

New Invariants For Entangled States, Roman V. Buniy, Thomas W. Kephart

Mathematics, Physics, and Computer Science Faculty Articles and Research

We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature.

Stochastic Processes Induced By Singular Operators, Daniel Alpay, Palle Jorgensen

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure σ on Rn. The case when σ is assumed absolutely continuous with respect to Lebesgue measure was stud- ied earlier in the literature, when n = 1. Our focus here is on showing how different equivalence classes (defined from relative absolute continuity for pairs of measures) translate into concrete spectral decompositions of the corresponding stochastic processes under study. The measures σ we consider are typically purely singular. Our proofs rely on the theory of (singular) unbounded operators in …

Influence Of Anomalous Dry Conditions On Aerosols Over India: Transport, Distribution And Properties, Dimitris G. Kaskaoutis, Ritesh Gautam, Ramesh P. Singh, E. E. Housos, D. Goto, S. Singh, A. Bartzokas, P. G. Kosmopoulos, Manish Sharma, N. C. Hsu, B. N. Holben, T. Takemura

Mathematics, Physics, and Computer Science Faculty Articles and Research

A synergy of satellite and ground-based radiometric observations, along with chemical transport modeling, was used for the assessment of the influence of drought monsoon conditions of 2002 and prolonged dry pre-monsoon period of 2003 on aerosol properties over south Asia, with emphasis over northern India. Reanalysis data are also examined for studying the dry anomalous period from the climatological mean, that show prevalence of westerlies under anticyclonic circulation and subsidence favoring the accumulation of aerosols. TRMM observations over south Asia indicate significant rainfall deficit over northwestern India in July 2002 and May-June 2003. Subsequently, the anomalous and prolonged dry conditions …

Schur Functions And Their Realizations In The Slice Hyperholomorphic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization …

New Topological C-Algebras With Applications In Linear Systems Theory, Daniel Alpay, Guy Salomon

Mathematics, Physics, and Computer Science Faculty Articles and Research

Motivated by the Schwartz space of tempered distributions S′ and the Kondratiev space of stochastic distributions S−1 we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces H′p,p∈N, with decreasing norms |⋅|p. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form |f∗g|p≤A(p−q)|f|q|g|p for all p≥q+d, where * denotes the convolution in the monoid, A(p−q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological C-algebras). Such an …

Impact Of Vegetation On Land-Atmosphere Coupling Strength And Its Implication For Desertification Mitigation Over East Asia, Boksoon Myoung, Yong-Sang Choi, Suk-Jin Choi, Seon Ki Park

Mathematics, Physics, and Computer Science Faculty Articles and Research

Desertification of the East Asian drylands and the consequent dust transport have been serious concerns for adjacent Asian countries as well as the western United States. Tree planting has been considered one applicable strategy to mitigate the desertification. However, the desired effect of the tree planting would not be brought to fruition unless the newly planted trees change the coupling characteristics between the land and the atmosphere. Based on this perception, we attempt to clarify the effects of vegetation on the coupling strength between the atmosphere and land surface, and we suggest the most efficient areas of tree planting for …

Personality Type Differences Between Ph.D. Climate Researchers And The General Public: Implications For Effective Communication, C. Susan Weiler, Jason K. Keller, Christina Olex

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Effectively communicating the complexity of climate change to the public is an important goal for the climate change research community, particularly for those of us who receive public funds. The challenge of communicating the science of climate change will be reduced if climate change researchers consider the links between personality types, communication tendencies and learning preferences. Jungian personality type is one of many factors related to an individual’s preferred style of taking in and processing information, i.e., preferred communication style. In this paper, we demonstrate that the Jungian personality type profile of interdisciplinary, early career climate researchers is significantly different …

Assessing Satellite-Based Rainfall Estimates In Semiarid Watersheds Using The Usda-Ars Walnut Gulch Gauge Network And Trmm Pr, Eyal Amitai, Carl L. Unkrich, David C. Goodrich, Emad Habib, Bryson Thill

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

The rain gauge network associated with the Walnut Gulch Experimental Watershed (WGEW) in southeastern Arizona provides a unique opportunity for direct comparisons of in situ measurements and satellite-based instantaneous rain rate estimates like those from the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR). The WGEW network is the densest rain gauge network in the PR coverage area for watersheds greater than 10 km(2). It consists of 88 weighing rain gauges within a 149-km(2) area. On average, approximately 10 gauges can be found in each PR field of view (similar to 5-km diameter). All gauges are very well synchronized with …

Coalgebraic Logics (Dagstuhl Seminar 12411), Ernst-Erich Doberkat, Alexander Kurz

Engineering Faculty Articles and Research

This report documents the program and the outcomes of Dagstuhl Seminar 12411 “Coalgebraic Logics”. The seminar deals with recent developments in the area of coalgebraic logic, a branch of logics which combines modal logics with coalgebraic semantics. Modal logic finds its uses when reasoning about behavioural and temporal properties of computation and communication, coalgebras have evolved into a general theory of systems. Consequently, it is natural to combine both areas for a mathematical description of system specification. Coalgebraic logics are closely related to the broader categories semantics/formal methods and verification/logic.

Strongly Complete Logics For Coalgebras, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary set-functor is given and proven to be strongly complete under additional assumptions. We proceed in three parts.

Part I argues that sifted colimit preserving functors are those functors that preserve universal algebraic structure. Our main theorem here states that a functor preserves sifted colimits if and only if it has a finitary presentation by operations and equations. Moreover, the presentation of the …

White Noise Based Stochastic Calculus Associated With A Class Of Gaussian Processes, Daniel Alpay, Haim Attia, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.

Integral Conditions For The Vanishing Of The Cohomology Of Open Sets In Cn, Fabrizio Colombo, M. E. Luna-Elizarrarás, Irene Sabadini, M. Shapiro, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we develop and extend some techniques introduced in [1] to find integral conditions for the vanishing of the cohomology of open bounded sets in Cn with values in the sheaf of holomorphic functions.

Teleportation In General Probabilistic Theories, Howard Barnum, Jonathan Barrett, Matthew S. Leifer, Alex Wilce

Mathematics, Physics, and Computer Science Faculty Articles and Research

In a previous paper, we showed that many important quantum information-theoretic phenomena, including the no-cloning and no-broadcasting theorems, are in fact generic in all non-classical probabilistic theories. An exception is teleportation, which most such theories do not support. In this paper, we investigate which probabilistic theories, and more particularly, which composite systems, do support a teleportation protocol. We isolate a natural class of composite systems that we term regular, and establish necessary and sufficient conditions for a regular tripartite system to support a conclusive, or post-selected, teleportation protocol. We also establish a sufficient condition for deterministic teleportation that yields …

Everything Is Entangled, Roman V. Buniy, Stephen D. H. Hsu

Mathematics, Physics, and Computer Science Faculty Articles and Research

We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other - the reduced density matrix describing any pair is likely to be separable.

Pbr, Epr, And All That Jazz, Matthew S. Leifer

Mathematics, Physics, and Computer Science Faculty Articles and Research

"In the past couple of months, the quantum foundations world has been abuzz about a new preprint entitled "The Quantum State Cannot be Interpreted Statistically" by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR). Since I wrote a blog post explaining the result, I have been inundated with more correspondence from scientists and more requests for comment from science journalists than at any other point in my career. Reaction to the result amongst quantum researchers has been mixed, with many people reacting negatively to the title, which can be misinterpreted as an attack on the Born rule. …