Measurement

This two-part activity provides an introduction to the basics of measurement (linear, mass, volume, density) and discusses the role of inferential statistics in comparing any two measurements. The concept of random variations in measurements is introduced, which leads to a discussion of binomial distributions and probability in comparing measurements and results. Students will use online databases to form null hypotheses and test them using an online t-test calculator. Links to datasets, an online statistical application, and to related sites are also provided. Educational levels: Undergraduate lower division, High school

Towards Designing a Performance Measurement System for the CGIAR : Draft Report

The System Office established the Working Group on Performance Measurement in May 2003, under the Co-Chairmanship of two ExCo members: Kevin Cleaver (ExCo/FC Chair) and Luis Arango (ExCo/PC member). Three sets of activities were carried out in preparation for the first meeting of the WG on September 5, 2003:(1) The CGIAR Secretariat prepared a Sourcebook on Performance Measurement in Research Institutions and Programs as background on approaches and methods of performance measurement being used in similar organizations globally.(2) Members of the WG shared additional information relevant to the objectives of the exercise (e.g., papers, articles);(3) A sub-group of the WG (made up of technical experts and resource persons1) met for a two day workshop on August 11-12, 2003 to discuss and outline performance measurement options that could be considered by the WG at its September 5 meeting, as a means of facilitating the task of the WG. This paper reflects the outcome of this preparatory workshop.The paper is organized as follows: the remainder of this chapter discusses the rationalebehind the worldwide trends towards Performance Measurement and offers definitions ofsome key terms. Chapter 2 focuses on the CGIAR, describing potential purposes and usesof performance measurement, identifying possible key elements of a performance measurement system, and outlining how such a system could fit into the planning and evaluation processes of the CGIAR. The final chapter summarizes the main conclusions and recommendations. This report was discussed during the Business Meeting at AGM 2003

Measurement of qutrits

We proposed the procedure of measuring the unknown state of the three-level system - the qutrit, which was realized as the arbitrary polarization state of the single-mode biphoton field. This procedure is accomplished for the set of the pure states of qutrits; this set is defined by the properties of SU(2) transformations, that are done by the polarization transformers.Comment: 9 pages, 9 figure

Experimental evaluation of non-classical correlations between measurement outcomes and target observable in a quantum measurement

In general, it is difficult to evaluate measurement errors when the initial and final conditions of the measurement make it impossible to identify the correct value of the target observable. Ozawa proposed a solution based on the operator algebra of observables which has recently been used in experiments investigating the error-disturbance trade-off of quantum measurements. Importantly, this solution makes surprisingly detailed statements about the relations between measurement outcomes and the unknown target observable. In the present paper, we investigate this relation by performing a sequence of two measurements on the polarization of a photon, so that the first measurement commutes with the target observable and the second measurement is sensitive to a complementary observable. While the initial measurement can be evaluated using classical statistics, the second measurement introduces the effects of quantum correlations between the non-commuting physical properties. By varying the resolution of the initial measurement, we can change the relative contribution of the non-classical correlations and identify their role in the evaluation of the quantum measurement. It is shown that the most striking deviation from classical expectations is obtained at the transition between weak and strong measurements, where the competition between different statistical effects results in measurement values well outside the range of possible eigenvalues.Comment: 11 pages, 6 figures, small corrections to setup figur

Precision metrology using weak measurements

Weak values and measurements have been proposed as means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology, namely, (Q1) Does post-selection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyse these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.Comment: 5+5 pages, 2 figure