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

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

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

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

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

Performance of the ARIANNA Hexagonal Radio Array

Installation of the ARIANNA Hexagonal Radio Array (HRA) on the Ross Ice Shelf of Antarctica has been completed. This detector serves as a pilot program to the ARIANNA neutrino telescope, which aims to measure the diffuse flux of very high energy neutrinos by observing the radio pulse generated by neutrino-induced charged particle showers in the ice. All HRA stations ran reliably and took data during the entire 2014-2015 austral summer season. A new radio signal direction reconstruction procedure is described, and is observed to have a resolution better than a degree. The reconstruction is used in a preliminary search for potential neutrino candidate events in the data from one of the newly installed detector stations. Three cuts are used to separate radio backgrounds from neutrino signals. The cuts are found to filter out all data recorded by the station during the season while preserving 85.4% of simulated neutrino events that trigger the station. This efficiency is similar to that found in analyses of previous HRA data taking seasons.Comment: Proceedings from the 34th ICRC2015, http://icrc2015.nl/ . 8 pages, 6 figure

A First Search for Cosmogenic Neutrinos with the ARIANNA Hexagonal Radio Array

The ARIANNA experiment seeks to observe the diffuse flux of neutrinos in the 10^8 - 10^10 GeV energy range using a grid of radio detectors at the surface of the Ross Ice Shelf of Antarctica. The detector measures the coherent Cherenkov radiation produced at radio frequencies, from about 100 MHz to 1 GHz, by charged particle showers generated by neutrino interactions in the ice. The ARIANNA Hexagonal Radio Array (HRA) is being constructed as a prototype for the full array. During the 2013-14 austral summer, three HRA stations collected radio data which was wirelessly transmitted off site in nearly real-time. The performance of these stations is described and a simple analysis to search for neutrino signals is presented. The analysis employs a set of three cuts that reject background triggers while preserving 90% of simulated cosmogenic neutrino triggers. No neutrino candidates are found in the data and a model-independent 90% confidence level Neyman upper limit is placed on the all flavor neutrino+antineutrino flux in a sliding decade-wide energy bin. The limit reaches a minimum of 1.9x10^-23 GeV^-1 cm^-2 s^-1 sr^-1 in the 10^8.5 - 10^9.5 GeV energy bin. Simulations of the performance of the full detector are also described. The sensitivity of the full ARIANNA experiment is presented and compared with current neutrino flux models.Comment: 22 pages, 22 figures. Published in Astroparticle Physic

Livetime and sensitivity of the ARIANNA Hexagonal Radio Array

The ARIANNA collaboration completed the installation of the hexagonal radio array (HRA) in December 2014, serving as a pilot program for a planned high energy neutrino telescope located about 110 km south of McMurdo Station on the Ross Ice Shelf near the coast of Antarctica. The goal of ARIANNA is to measure both diffuse and point fluxes of astrophysical neutrinos at energies in excess of 1016 eV. Upgraded hardware has been installed during the 2014 deployment season and stations show a livetime of better than 90% between commissioning and austral sunset. Though designed to observe radio pulses from neutrino interactions originating within the ice below each detector, one station was modified to study the low-frequency environment and signals from above. We provide evidence that the HRA observed both continuous emission from the Galaxy and a transient solar burst. Preliminary work on modeling the (weak) Galactic signal confirm the absolute sensitivity of the HRA detector system.Comment: Proceedings from the 34th ICRC2015, http://icrc2015.nl/, 8 pages, 6 figure

Almost uniform sampling via quantum walks

Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic Markov chain $P$ on $S$ for long enough to obtain a random state from within $\epsilon$ total variation distance of the uniform distribution over $S$. The running time of this algorithm, the so-called {\em mixing time} of $P$, is $O(\delta^{-1} (\log N + \log \epsilon^{-1}))$, where $\delta$ is the spectral gap of $P$. We present a natural quantum version of this algorithm based on repeated measurements of the {\em quantum walk} $U_t = e^{-iPt}$. We show that it samples almost uniformly from $S$ with logarithmic dependence on $\epsilon^{-1}$ just as the classical walk $P$ does; previously, no such quantum walk algorithm was known. We then outline a framework for analyzing its running time and formulate two plausible conjectures which together would imply that it runs in time $O(\delta^{-1/2} \log N \log \epsilon^{-1})$ when $P$ is the standard transition matrix of a constant-degree graph. We prove each conjecture for a subclass of Cayley graphs.Comment: 13 pages; v2 added NSF grant info; v3 incorporated feedbac

Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search

By applying Grover's quantum search algorithm to the lattice algorithms of Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and Stehl\'{e}, we obtain improved asymptotic quantum results for solving the shortest vector problem. With quantum computers we can provably find a shortest vector in time $2^{1.799n + o(n)}$, improving upon the classical time complexity of $2^{2.465n + o(n)}$ of Pujol and Stehl\'{e} and the $2^{2n + o(n)}$ of Micciancio and Voulgaris, while heuristically we expect to find a shortest vector in time $2^{0.312n + o(n)}$, improving upon the classical time complexity of $2^{0.384n + o(n)}$ of Wang et al. These quantum complexities will be an important guide for the selection of parameters for post-quantum cryptosystems based on the hardness of the shortest vector problem.Comment: 19 page