Characterizing Nonclassical Correlations via Local Quantum Uncertainty

Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. Here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. When revealed on local observables of a bipartite system, such uncertainty defines an entire class of bona fide measures of nonclassical correlations. For the case of 2 x d systems, we find that a unique measure is defined, which we evaluate in closed form. We then discuss the role that these correlations, which are of the 'discord' type, can play in the context of quantum metrology. We show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision, as quantified by the quantum Fisher information, in the optimal phase estimation protocol.Comment: Published in PRL, Editors' Suggestio

Discovering the roots: Uniform closure results for algebraic classes under factoring

Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this form, the process yields a better circuit complexity in the case when the number of roots $r$ is small but the multiplicities are exponentially large. Our method sets up a linear system in $r$ unknowns and iteratively builds the roots as formal power series. For an algebraic circuit $f(x_1,\ldots,x_n)$ of size $s$ we prove that each factor has size at most a polynomial in: $s$ and the degree of the squarefree part of $f$. Consequently, if $f_1$ is a $2^{\Omega(n)}$-hard polynomial then any nonzero multiple $\prod_{i} f_i^{e_i}$ is equally hard for arbitrary positive $e_i$'s, assuming that $\sum_i \text{deg}(f_i)$ is at most $2^{O(n)}$. It is an old open question whether the class of poly($n$)-sized formulas (resp. algebraic branching programs) is closed under factoring. We show that given a polynomial $f$ of degree $n^{O(1)}$ and formula (resp. ABP) size $n^{O(\log n)}$ we can find a similar size formula (resp. ABP) factor in randomized poly($n^{\log n}$)-time. Consequently, if determinant requires $n^{\Omega(\log n)}$ size formula, then the same can be said about any of its nonzero multiples. As part of our proofs, we identify a new property of multivariate polynomial factorization. We show that under a random linear transformation $\tau$, $f(\tau\overline{x})$ completely factors via power series roots. Moreover, the factorization adapts well to circuit complexity analysis. This with allRootsNI are the techniques that help us make progress towards the old open problems, supplementing the large body of classical results and concepts in algebraic circuit factorization (eg. Zassenhaus, J.NT 1969, Kaltofen, STOC 1985-7 \& Burgisser, FOCS 2001).Comment: 33 Pages, No figure

Strength Modeling Report

Strength modeling is a complex and multi-dimensional issue. There are numerous parameters to the problem of characterizing human strength, most notably: (1) position and orientation of body joints; (2) isometric versus dynamic strength; (3) effector force versus joint torque; (4) instantaneous versus steady force; (5) active force versus reactive force; (6) presence or absence of gravity; (7) body somatotype and composition; (8) body (segment) masses; (9) muscle group envolvement; (10) muscle size; (11) fatigue; and (12) practice (training) or familiarity. In surveying the available literature on strength measurement and modeling an attempt was made to examine as many of these parameters as possible. The conclusions reached at this point toward the feasibility of implementing computationally reasonable human strength models. The assessment of accuracy of any model against a specific individual, however, will probably not be possible on any realistic scale. Taken statistically, strength modeling may be an effective tool for general questions of task feasibility and strength requirements

What causes differences in achievement in Zimbabwe's secondary schools?

The authors found that students who attended high-fee-paying (trust) schools, elite urban governments schools, and mission schools scored better in mathematics and English achievement than did students in the less-well-endowed government schools and those established by local councils. Much of the variation in the student achievement was attributable to the schools the student attended. Examination results were higher in schools with a high proportion of trained teachers, with a good supply of textbooks, and with a stable faculty (high teacher retention). But once researcher control for these factors, contrary to expectations, some underendowed local council and government schools are more effective at boosting achievement than their counterparts with more resources. So, textbooks and teachers are important in raising achievement, but more research is needed into what characteristics differentiate high-achieving schools from low-achieving schools.Teaching and Learning,Gender and Education,Primary Education,Health Monitoring&Evaluation,Girls Education

Macroeconomic effects of terms-of-trade shocks : the case of oil-exporting countries

The authors investigate the impact on economic growth and development of long-run movements in the external terms of trade, with special reference to the experience of 18 oil-exporting countries between 1973 and 1989. They argue that this sample approximates a controlled experiment for examining the impact of unanticipated -- but permanent -- shocks to the terms of trade. They analyze the sample econometrically using panel data techniques. They find that permanent terms-of-trade shocks have a strongly significant positive effect on investment, which they justify theoretically on the grounds that countries in the sample import much of their capital equipment. The shocks also have a significant positive effect on consumption. Government consumption responds almost twice as strongly as private consumption. The shocks have no effect on savings and adversely affect the trade and current account balances. There is a significant positive effect on the output of all main categories of nontradables. But Dutch disease effects are strikingly absent. Agriculture and manufacturing do not contract in reaction to an oil price increase. Dutch disease effects may be absent in part because of policy-induced output restraints in the oil sector, or because of the"enclave"nature of the oil sector, which does not participate in domestic factor markets.Economic Theory&Research,Environmental Economics&Policies,Payment Systems&Infrastructure,Labor Policies,Financial Intermediation,Environmental Economics&Policies,Economic Theory&Research,TF054105-DONOR FUNDED OPERATION ADMINISTRATION FEE INCOME AND EXPENSE ACCOUNT,Financial Intermediation,Inequality

Model Invalidation: A Connection between Robust Control and Identification

This paper begins to address the gap between the models used in robust control theory and those obtained from identification experiments by considering the connection between uncertain models and data. The model invalidation problem considered here is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the input/output data