Uncertainty Relation for the Discrete Fourier Transform

We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=exp[i phi] VU. Its most important application is to constrain how much a quantum state can be localised simultaneously in two mutually unbiased bases related by a Discrete Fourier Transform. It provides an uncertainty relation which smoothly interpolates between the well known cases of the Pauli operators in 2 dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the Harmonic oscillator equation.Comment: Extended Version; 13 pages; In press in Phys. Rev. Let

Web Surveys (Version 2.0)

This contribution addresses fundamental methodological problems facing online surveys, especially the coverage problem and sample-selection issues. The use of online panels based on random samples is seen as a possible solution

Measurement of very small phase fluctuations by means of the operational approach

Recently Noh, Fourgeres and Mandel (NFM) have improved the operational approach to the quantum phase problem substantially and measured the phase dispersion of coherent light down to very small means photon numbers of the order of 10(exp -2). This has prompted many other investigations and clarified some important questions in relation to what is actually measured. Although their treatment is rather general, we confine ourselves here to the case of a strong local oscillator (LO) and reproduce their measurement scheme. Surprisingly enough, this simultaneous measurement of the sine and the cosine of the phase difference is completely equivalent to an old proposal to measure the phase after strong linear amplification realized experimentally by the Welling group. The reason for this rests on the fact, that in both cases the results are determined by the Q function of the signal. This was shown for amplification in and for the measurement after beam splitting by Lai and Haus

Online-Befragung (Version 1.1)

Der Beitrag behandelt grundlegende methodische Probleme bei Online-Befragungen, insbesondere das Coverage-Problem und Fragen der Stichprobenziehung. Lösungsmöglichkeiten werden im Einsatz von Access Panels auf der Basis von Zufallsstichproben gesehen

Item comparability in cross-national surveys: results from asking probing questions in cross-national web surveys about attitudes towards civil disobedience

This article focuses on assessing item comparability in cross-national surveys by asking probing questions in Web surveys. The "civil disobedience" item from the "rights in a democracy" scale of the International Social Survey Program (ISSP) serves as a substantive case study. Identical Web surveys were fielded in Canada (English-speaking), Denmark, Germany, Hungary, Spain, and the U.S. A category-selection and a comprehension probe, respectively, were incorporated into the Web surveys after the closed-ended "civil disobedience" item. Responses to the category selection-probe reveal that notably in Germany, Hungary, and Spain the detachment of politicians from the people and their lack of responsiveness is deplored. Responses to the comprehension probe show that mainly in the U.S. and Canada violence and/or destruction are associated with civil disobedience. These results suggest reasons for the peculiar statistical results found for the "civil disobedience" item in the ISSP study. On the whole, Web probing proves to be a valuable tool for identifying interpretation differences and potential bias in cross-national survey research

Number phase uncertainty relations: verification by homodyning

It is shown that fundamental uncertainty relations between photon number and canonical phase of a single-mode optical field can be verified by means of balanced homodyne measurement. All the relevant quantities can be sampled directly from the measured phase-dependent quadrature distribution.Comment: 1 Ps figure (divided in 3 subfigures) using REVTE

Asking probing questions in web surveys: which factors have an impact on the quality of responses?

Cognitive interviewing is a well-established method for evaluating and improving a questionnaire prior to fielding. However, its present implementation brings with it some challenges, notably in terms of small sample sizes or the possibility of interviewer effects. In this study, the authors test web surveys through nonprobability online panels as a supplemental means to implement cognitive interviewing techniques. The overall goal is to tackle the above-mentioned challenges. The focus in this article is on methodological features that pave the way for an eventual successful implementation of category-selection probing in web surveys. The study reports on the results of 1,023 respondents from Germany. In order to identify implementation features that lead to a high number of meaningful answers, the authors explore the effects of (1) different panels, (2) different probing variants, and (3) different numbers of preceding probes on answer quality. The overall results suggest that category-selection probing can indeed be implemented in web surveys. Using data from two panels - a community panel where members can actively get involved, for example, by creating their own polls, and a "conventional" panel where answering surveys is the members' only activity - the authors find that high community involvement does not increase the likelihood to answer probes or produce longer statements. Testing three probing variants that differ in wording and provided context, the authors find that presenting the context of the probe (i.e., the probed item and the respondent's answer) produces a higher number of meaningful answers. Finally, the likelihood to answer a probe decreases with the number of preceding probes. However, the word count of those who eventually answer the probes slightly increases with an increasing number of probes. (author's abstract