The Optimal Single Copy Measurement for the Hidden Subgroup Problem

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup problem. Previous work has identified the optimal single copy measurement for the hidden subgroup problem over abelian groups as well as for the non-abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single copy measurement for the hidden subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single copy optimal measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe

The Potential Wind Power Resource in Australia: A New Perspective

Australia is considered to have very good wind resources, and the utilization of this renewable energy resource is increasing. Wind power installed capacity increased by 35% from 2006 to 2011 and is predicted to account for over 12% of Australia’s electricity generation in 2030. This study uses a recently published methodology to address the limitations of previous wind resource analyses, and frames the nature of Australia’s wind resources from the perspective of economic viability, using robust metrics of the abundance, variability and intermittency of wind power density, and analyzes whether these differ with higher wind turbine hub heights. We also assess the extent to which wind intermittency can potentially be mitigated by the aggregation of geographically dispersed wind farms. Our results suggest that over much of Australia, areas that have high wind intermittency coincide with large expanses in which the aggregation of turbine output does not mitigate variability. These areas are also geographically remote, some are disconnected from the east coast’s electricity grid and large population centers, and often are not connected or located near enough to high capacity electricity infrastructure, all of which would decrease the potential economic viability of wind farms in these locations. However, on the eastern seaboard, even though the wind resource is weaker, it is less variable, much closer to large population centers, and there exists more potential to mitigate its intermittency through aggregation.The authors gratefully acknowledge the financial support for this work provided by the MIT Joint Program on the Science and Policy of Global Change through a number of federal agencies and industrial sponsors including US Department of Energy grant DE-FG02-94ER61937

Including Systematic Uncertainties in Confidence Interval Construction for Poisson Statistics

One way to incorporate systematic uncertainties into the calculation of confidence intervals is by integrating over probability density functions parametrizing the uncertainties. In this note we present a development of this method which takes into account uncertainties in the prediction of background processes, uncertainties in the signal detection efficiency and background efficiency and allows for a correlation between the signal and background detection efficiencies. We implement this method with the Feldman & Cousins unified approach with and without conditioning. We present studies of coverage for the Feldman & Cousins and Neyman ordering schemes. In particular, we present two different types of coverage tests for the case where systematic uncertainties are included. To illustrate the method we show the relative effect of including systematic uncertainties the case of dark matter search as performed by modern neutrino tel escopes.Comment: 23 pages, 10 figures, replaced to match published versio

An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of size p3 and exponent p. Exploiting certain nice automorphisms of the extraspecial groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealt with directly.Comment: 10 page

ARIS-Campaign: intercomparison of three ground based 22 GHz radiometers for middle atmospheric water vapor at the Zugspitze in winter 2009

This paper presents the Alpine Radiometer Intercomparison at the Schneefernerhaus (ARIS), which took place in winter 2009 at the high altitude station at the Zugspitze, Germany (47.42° N, 10.98° E, 2650 m). This campaign was the first direct intercomparison between three new ground based 22 GHz water vapor radiometers for middle atmospheric profiling with the following instruments participating: MIRA 5 (Karlsruhe Institute of Technology), cWASPAM3 (Max Planck Institute for Solar System Research, Katlenburg-Lindau) and MIAWARA-C (Institute of Applied Physics, University of Bern). Even though the three radiometers all measure middle atmospheric water vapor using the same rotational transition line and similar fundamental set-ups, there are major differences between the front ends, the back ends, the calibration concepts and the profile retrieval. The spectrum comparison shows that all three radiometers measure spectra without severe baseline artifacts and that the measurements are in good general agreement. The measurement noise shows good agreement to the values theoretically expected from the radiometer noise formula. At the same time the comparison of the noise levels shows that there is room for instrumental and calibration improvement, emphasizing the importance of low elevation angles for the observation, a low receiver noise temperature and an efficient calibration scheme. <br><br> The comparisons of the retrieved profiles show that the agreement between the profiles of MIAWARA-C and cWASPAM3 with the ones of MLS is better than 0.3 ppmv (6%) at all altitudes. MIRA 5 has a dry bias of approximately 0.5 ppm (8%) below 0.1 hPa with respect to all other instruments. The profiles of cWASPAM3 and MIAWARA-C could not be directly compared because the vertical region of overlap was too small. The comparison of the time series at different altitude levels show a similar evolution of the H<sub>2</sub>O volume mixing ratio (VMR) for the ground based instruments as well as the space borne sensor MLS

Computational Indistinguishability between Quantum States and Its Cryptographic Application

We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem, QSCDff, is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show that QSCDff has three properties of cryptographic interest: (i) QSCDff has a trapdoor; (ii) the average-case hardness of QSCDff coincides with its worst-case hardness; and (iii) QSCDff is computationally at least as hard as the graph automorphism problem in the worst case. These cryptographic properties enable us to construct a quantum public-key cryptosystem, which is likely to withstand any chosen plaintext attack of a polynomial-time quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies on similar cryptographic properties of QSCDcyc.Comment: 24 pages, 2 figures. We improved presentation, and added more detail proofs and follow-up of recent wor

Diurnal salivary cortisol concentrations in Parkinson’s disease: increased total secretion and morning cortisol concentrations

Background:Parkinson’s disease (PD) is a chronic neurodegenerative disorder. There is limited knowledge about the function of the hypothalamic-pituitary-adrenal axis in PD. The primary aim of this prospective study was to analyze diurnal salivary cortisol concentrations in patients with PD and correlate these with age, gender, body mass index (BMI), duration of PD, and pain. The secondary aim was to compare the results with a healthy reference group. Methods:Fifty-nine PD patients, 35 women and 24 men, aged 50–79 years, were recruited. The reference group comprised healthy individuals matched for age, gender, BMI, and time point for sampling. Salivary cortisol was collected at 8 am, 1 pm, and 8 pm, and 8 am the next day using cotton-based Salivette ®tubes and analyzed using Spectria®Cortisol I125. A visual analog scale was used for estimation of pain. Results:The median cortisol concentration was 16.0 (5.8–30.2) nmol/L at 8 am, 5.8 (3.0–16.4) at 1 pm, 2.8 (1.6–8.0) at 8 pm, and 14.0 (7.5–28.7) at 8 am the next day. Total secretion and rate of cortisol secretion during the day (8 am–8 pm) and the concentration of cortisol on the next morning were lower (12.5 nmol/L) in the reference group. No significant correlations with age, gender, BMI, duration of PD, Hoehn and Yahr score, Unified Parkinson’s Disease Rating Scale III score, gait, pain, or cortisol concentrations were found. Conclusion:The neurodegenerative changes in PD does not seem to interfere with the hypothalamic-pituitary-adrenal axis. Salivary cortisol concentrations in PD patients were increased in the morning compared with the reference group, and were not influenced by motor dysfunction, duration of disease, or coexistence of chronic or acute pain