Novelty, efficacy, and significance of weak measurements for quantum tomography

© 2015 American Physical Society. The use of weak measurements for performing quantum tomography is enjoying increased attention due to several recent proposals. The claimed merits of using weak measurements in this context are varied, but are generally represented by novelty, increased efficacy, and foundational significance. We critically evaluate two proposals that make such claims and find that weak measurements are not an essential ingredient for most of their claimed features

Fisher-Symmetric Informationally Complete Measurements for Pure States

© 2016 American Physical Society. We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that uniquely represent pure quantum states in the neighborhood of a fiducial pure state. The measurement is locally informationally complete - i.e., it uniquely determines these parameters, as opposed to distinguishing two arbitrary quantum states - and it is maximal in the sense of a multiparameter quantum Cramér-Rao bound. For a d-dimensional quantum system, requiring only local informational completeness allows us to reduce the number of outcomes of the measurement from a minimum close to but below 4d-3, for the usual notion of global pure-state informational completeness, to 2d-1

Infrared behavior of interacting bosons at zero temperature

We review the infrared behavior of interacting bosons at zero temperature. After a brief discussion of the Bogoliubov approximation and the breakdown of perturbation theory due to infrared divergences, we present two approaches that are free of infrared divergences -- Popov's hydrodynamic theory and the non-perturbative renormalization group -- and allow us to obtain the exact infrared behavior of the correlation functions. We also point out the connection between the infrared behavior in the superfluid phase and the critical behavior at the superfluid--Mott-insulator transition in the Bose-Hubbard model.Comment: 8 pages, 4 figures. Proceedings of the 19th International Laser Physics Workshop, LPHYS'10 (Foz do Iguacu, Brazil, July 5-9, 2010

Lectures on Spectrum Generating Symmetries and U-duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace

We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their U-duality groups. For 5D, N=2 Maxwell-Einstein supergravity theories (MESGT) defined by Euclidean Jordan algebras, J, the spectrum generating symmetry groups are the conformal groups Conf(J) of J which are isomorphic to their U-duality groups in four dimensions. Similarly, the spectrum generating symmetry groups of 4D, N=2 MESGTs are the quasiconformal groups QConf(J) associated with J that are isomorphic to their U-duality groups in three dimensions. We then review the work on spectrum generating symmetries of spherically symmetric stationary 4D BPS black holes, based on the equivalence of their attractor equations and the equations for geodesic motion of a fiducial particle on the target spaces of corresponding 3D supergravity theories obtained by timelike reduction. We also discuss the connection between harmonic superspace formulation of 4D, N=2 sigma models coupled to supergravity and the minimal unitary representations of their isometry groups obtained by quantizing their quasiconformal realizations. We discuss the relevance of this connection to spectrum generating symmetries and conclude with a brief summary of more recent results.Comment: 55 pages; Latex fil

Measurement differences in the assessment of functional limitations for cognitive impairment classification across geographic locations

Introduction: The measurement of dementia in cross-national contexts relies on the assessment of functional limitations. We aimed to evaluate the performance of survey items on functional limitations across culturally diverse geographic settings. Methods: We used data from the Harmonized Cognitive Assessment Protocol Surveys (HCAP) in five countries (total N = 11,250) to quantify associations between items on functional limitations and cognitive impairment. Results: Many items performed better in the United States and England compared to South Africa, India, and Mexico. Items on the Community Screening Instrument for Dementia (CSID) had the least variability across countries (SD = 0.73 vs. 0.92 [Blessed] and 0.98 [Jorm IQCODE]), but also the weakest associations with cognitive impairment (median odds ratio [OR] = 2.23 vs. 3.01 [Blessed] and 2.75 [Jorm IQCODE]). Discussion: Differences in cultural norms for reporting functional limitations likely influences performance of items on functional limitations and may affect the interpretation of results from substantive studies. Highlights: There was substantial cross-country variation in item performance. Items from the Community Screening Instrument for Dementia (CSID) had less cross-country variability but lower performance. There was more variability in performance of instrumental activities of daily living (IADL) compared to activities of daily living (ADL) items. Variability in cultural expectations of older adults should be taken into account. Results highlight the need for novel approaches to assessing functional limitations

Computing Linear Matrix Representations of Helton-Vinnikov Curves

Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a geometric approach via contact curves, and an analytic approach via theta functions. These are explained, compared, and tested experimentally for low degree instances.Comment: 19 pages, 3 figures, minor revisions; Mathematical Methods in Systems, Optimization and Control, Birkhauser, Base

Dynamical mass generation in quantum field theory : some methods with application to the Gross-Neveu model and Yang-Mills theory

We introduce some techniques to investigate dynamical mass generation. The Gross-Neveu model (GN) is used as a toy model, because the GN mass gap is exactly known, making it possible to check reliability of the various methods. Very accurate results are obtained. Also application to SU(N) Yang-Mills (YM) is discussed.Comment: 8 LaTeX2e pages, uses Kluwer class file crckbked.cls. Kluwer package included. To appear in: Proceedings of the NATO Advanced Research Workshop on "Confinement, Topology, and other Non-Perturbative Aspects of QCD", Stara Lesna, Slovakia, 21-27 jan 200

First-trimester or second-trimester screening, or both, for Down's syndrome

BACKGROUND: It is uncertain how best to screen pregnant women for the presence of fetal Down's syndrome: to perform first-trimester screening, to perform second-trimester screening, or to use strategies incorporating measurements in both trimesters.METHODS: Women with singleton pregnancies underwent first-trimester combined screening (measurement of nuchal translucency, pregnancy-associated plasma protein A [PAPP-A], and the free beta subunit of human chorionic gonadotropin at 10 weeks 3 days through 13 weeks 6 days of gestation) and second-trimester quadruple screening (measurement of alpha-fetoprotein, total human chorionic gonadotropin, unconjugated estriol, and inhibin A at 15 through 18 weeks of gestation). We compared the results of stepwise sequential screening (risk results provided after each test), fully integrated screening (single risk result provided), and serum integrated screening (identical to fully integrated screening, but without nuchal translucency).RESULTS: First-trimester screening was performed in 38,167 patients; 117 had a fetus with Down's syndrome. At a 5 percent false positive rate, the rates of detection of Down's syndrome were as follows: with first-trimester combined screening, 87 percent, 85 percent, and 82 percent for measurements performed at 11, 12, and 13 weeks, respectively; with second-trimester quadruple screening, 81 percent; with stepwise sequential screening, 95 percent; with serum integrated screening, 88 percent; and with fully integrated screening with first-trimester measurements performed at 11 weeks, 96 percent. Paired comparisons found significant differences between the tests, except for the comparison between serum integrated screening and combined screening.CONCLUSIONS: First-trimester combined screening at 11 weeks of gestation is better than second-trimester quadruple screening but at 13 weeks has results similar to second-trimester quadruple screening. Both stepwise sequential screening and fully integrated screening have high rates of detection of Down's syndrome, with low false positive rates

Noncommutative Vortices and Instantons from Generalized Bose Operators

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.Comment: 25 page

KK6 from M2 in BLG

We study the possibility that the Kaluza-Klein monopole (KK6) world-volume action may be obtained from the multiple membranes (M2) action which is described by BLG theory. We first point out that the infinite dimensional Lie 3-algebra based on the Nambu-Poisson structure could not only provide three dimensional manifolds to allow M5 from M2, which was studied by previous authors, but also provide five dimensional manifolds to allow KK6 from M2. We next present a possible way that the U(1) field on KK6 world-volume action could be produced form the gauge potential in BLG theory.Comment: Latex, 15 pages. V3: Add theorem 2 to complete proof. V4: Detail physical interpretations and calculations in section