MEASUREMENT OF RELATIVE POVERTY

Food Security and Poverty,

Measurement uncertainty relations for position and momentum: Relative entropy formulation

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be quantified in various ways. The relative entropy is the natural theoretical quantifier of the information loss when a `true' probability distribution is replaced by an approximating one. In this paper, we provide a lower bound for the amount of information that is lost by replacing the distributions of the sharp position and momentum observables, as they could be obtained with two separate experiments, by the marginals of any smeared joint measurement. The bound is obtained by introducing an entropic error function, and optimizing it over a suitable class of covariant approximate joint measurements. We fully exploit two cases of target observables: (1) $n$-dimensional position and momentum vectors; (2) two components of position and momentum along different directions. In (1), we connect the quantum bound to the dimension $n$; in (2), going from parallel to orthogonal directions, we show the transition from highly incompatible observables to compatible ones. For simplicity, we develop the theory only for Gaussian states and measurements.Comment: 33 page

Research relative to weather radar measurement techniques

Research relative to weather radar measurement techniques, which involves some investigations related to measurement techniques applicable to meteorological radar systems in Thailand, is reported. A major part of the activity was devoted to instruction and discussion with Thai radar engineers, technicians, and meteorologists concerning the basic principles of radar meteorology and applications to specific problems, including measurement of rainfall and detection of wind shear/microburst hazards. Weather radar calibration techniques were also considered during this project. Most of the activity took place during two visits to Thailand, in December 1990 and February 1992

Research relative to weather radar measurement techniques

This grant provides for some investigations related to weather radar measurement techniques applicable to meteorological radar systems in Thailand. Quality data are needed from those systems to support TRMM and other scientific investigations. Activities carried out during a trip to the radar facilities at Phuket are described

Measurement of relative phase diffusion between two Bose-Einstein condensates

We propose a method of measuring diffusion of the relative phase between two Bose-Einstein condensates occupying different nuclear or spin hyperfine states coupled by a two-photon transition via an intermediate level. Due to the macroscopic quantum coherence the condensates can be decoupled from the electromagnetic fields. The rate of decoherence and the phase collapse may be determined from the occupation of the intermediate level or the absorption of radiation.Comment: 4 pages, RevTex, 2 ps figure

On Variational Expressions for Quantum Relative Entropies

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback-Leibler divergence over projective measurement statistics, is strictly smaller than Umegaki's quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petz' conclusion remains true if we allow general positive operator valued measures. Second, we extend the result to Renyi relative entropies and show that for non-commuting states the sandwiched Renyi relative entropy is strictly larger than the measured Renyi relative entropy for $\alpha \in (\frac12, \infty)$, and strictly smaller for $\alpha \in [0,\frac12)$. The latter statement provides counterexamples for the data-processing inequality of the sandwiched Renyi relative entropy for $\alpha < \frac12$. Our main tool is a new variational expression for the measured Renyi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive.Comment: v2: final published versio

Differential electron flux as determined by auroral observations of the N2 positive and N2/+/ systems

Measurement of relative emission rates of auroral system