Analytical Blowup Solutions to the Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity in R^N

We study the N-dimensional pressureless Navier--Stokes-Poisson equations with density-dependent viscosity. With the extension of the blowup solutions for the Euler-Poisson equations, the analytical blowup solutions,in radial symmetry, in R^N are constructed.Comment: 12 Pages, more detail in the introduction to explain the validity of the mode

Classical capacity of the lossy bosonic channel: the exact solution

The classical capacity of the lossy bosonic channel is calculated exactly. It is shown that its Holevo information is not superadditive, and that a coherent-state encoding achieves capacity. The capacity of far-field, free-space optical communications is given as an example.Comment: 4 pages, 2 figures (revised version

Supplementary use of HbA1c as hyperglycemic criterion to detect metabolic syndrome

Background: Metabolic syndrome (MetS) refers to a cluster of cardiovascular risk factors including hyperglycemia, dyslipidemia, abdominal obesity and hypertension. An effective detection of MetS not only reflects the prediction risk of diabetes mellitus and cardiovascular diseases but also helps to plan for management strategy which could reduce the healthcare burden of the society. This study aimed to compare the use of hemoglobin A1c (HbA1c) to fasting plasma glucose (FPG) as the hyperglycemic component in MetS diagnosis. Methods: Waist circumference, blood pressure, blood triglyceride, high-density lipoprotein (HDL)-cholesterol, FPG, and HbA1c were examined in 120 Hong Kong Chinese adults with MetS and 120 without MetS. After reviewing the subject basal characteristics, 11 of them were found with undiagnosed diabetes (FPG ≧7.0 mmol/L) and were excluded for further analysis. Results: The most prevalent MetS components among the included subjects were elevated systolic blood pressure and central obesity. Significant correlation relationships existed between FPG and HbA1c in both subject pools diagnosed with and without MetS (p < 0.001). The diagnostic rate of MetS using HbA1c was compared to FPG by the receiver operating characteristics (ROC) analysis which suggested an area under curve of 0.807 (95% CI: 0.727 to 0.887). The agreement was 90.7% in MetS-positive group with increased FPG as one of the criterion co-existed with elevated HbA1c. If including HbA1c as an additional criterion to FPG in the MetS diagnosis, 30 more participants in MetS-negative group would be MetS-positive leading to an increase in detection rate. Furthermore, 47 subjects (38 from MetS-positive group and 9 from MetS-negative group) were found having HbA1c ≧6.5%, who would have been diagnosed with diabetes based on the diagnostic criteria implemented by the Expert Group in 2009. Conclusion: These findings suggest that HbA1c enhances the detection of hyperglycemia for the diagnosis of MetS.Department of Health Technology and Informatic

On the Relationship between Resolution Enhancement and Multiphoton Absorption Rate in Quantum Lithography

The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a ``NOON'' quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated, in order to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.Comment: 14 pages, 7 figures, submitted, v2: rewritten in response to referees' comments, v3: rewritten and extended, v4: accepted by Physical Review

Phase measurements with weak reference pulses

Quantum state discrimination for two coherent states with opposite phases as measured relative to a reference pulse is analyzed as functions of the intensities of both the signal states and of the reference pulse. This problem is relevant for Quantum Key Distribution with phase encoding. We consider both the optimum measurements and simple measurements that require only beamsplitters and photodetectors.Comment: 5 pages, 5 figures. I apologize for this boring pape

Measuring the quantum statistics of an atom laser beam

We propose and analyse a scheme for measuring the quadrature statistics of an atom laser beam using extant optical homodyning and Raman atom laser techniques. Reversal of the normal Raman atom laser outcoupling scheme is used to map the quantum statistics of an incoupled beam to an optical probe beam. A multimode model of the spatial propagation dynamics shows that the Raman incoupler gives a clear signal of de Broglie wave quadrature squeezing for both pulsed and continuous inputs. Finally, we show that experimental realisations of the scheme may be tested with existing methods via measurements of Glauber's intensity correlation function.Comment: 4 pages, 3 figure

Minimum-error discrimination between subsets of linearly dependent quantum states

A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal quantum states occurring with given a priori probabilities. A general analytical solution is obtained for N states that are restricted to a two-dimensional subspace of the Hilbert space of the system. The result for the special case of three arbitrary but linearly dependent states is applied to a variety of sets of three states that are symmetric and equally probable. It is found that, in this case, the minimum error probability for distinguishing one of the states from the other two is only about half as large as the minimum error probability for distinguishing all three states individually.Comment: Representation improved and generalized, references added. Accepted as a Rapid Communication in Phys. Rev.

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated by Heisenberg's thought experiment using a gamma-ray microscope. Here I show that this common assumption is false: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck's constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg's lower bound for the noise-disturbance product is violated even by a nearly nondisturbing, precise position measuring instrument. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.Comment: Revtex, 6 page

Does nonlinear metrology offer improved resolution? Answers from quantum information theory

A number of authors have suggested that nonlinear interactions can enhance resolution of phase shifts beyond the usual Heisenberg scaling of 1/n, where n is a measure of resources such as the number of subsystems of the probe state or the mean photon number of the probe state. These suggestions are based on calculations of `local precision' for particular nonlinear schemes. However, we show that there is no simple connection between the local precision and the average estimation error for these schemes, leading to a scaling puzzle. This puzzle is partially resolved by a careful analysis of iterative implementations of the suggested nonlinear schemes. However, it is shown that the suggested nonlinear schemes are still limited to an exponential scaling in \sqrt{n}. (This scaling may be compared to the exponential scaling in n which is achievable if multiple passes are allowed, even for linear schemes.) The question of whether nonlinear schemes may have a scaling advantage in the presence of loss is left open. Our results are based on a new bound for average estimation error that depends on (i) an entropic measure of the degree to which the probe state can encode a reference phase value, called the G-asymmetry, and (ii) any prior information about the phase shift. This bound is asymptotically stronger than bounds based on the variance of the phase shift generator. The G-asymmetry is also shown to directly bound the average information gained per estimate. Our results hold for any prior distribution of the shift parameter, and generalise to estimates of any shift generated by an operator with discrete eigenvalues.Comment: 8 page