The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states

Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses given a large number of observations. Recently the combined work of Audenaert et al. [Phys. Rev. Lett. 98, 160501] and Nussbaum and Szkola [quant-ph/0607216] has proved the quantum analog of this bound, which applies when the hypotheses correspond to two quantum states. Based on the quantum Chernoff bound, we define a physically meaningful distinguishability measure and its corresponding metric in the space of states; the latter is shown to coincide with the Wigner-Yanase metric. Along the same lines, we define a second, more easily implementable, distinguishability measure based on the error probability of discrimination when the same local measurement is performed on every copy. We study some general properties of these measures, including the probability distribution of density matrices, defined via the volume element induced by the metric, and illustrate their use in the paradigmatic cases of qubits and Gaussian infinite-dimensional states.Comment: 16 page

Generating nonclassical correlations without fully aligning measurements

We investigate the scenario where spatially separated parties perform measurements in randomly chosen bases on an N-partite Greenberger-Horne-Zeilinger state. We show that without any alignment of the measurements, the observers will obtain correlations that violate a Bell inequality with a probability that rapidly approaches 1 as N increases and that this probability is robust against noise. We also prove that restricting these randomly chosen measurements to a plane perpendicular to a common direction will always generate correlations that violate some Bell inequality. Specifically, if each observer chooses their two measurements to be locally orthogonal, then the N observers will violate one of two Bell inequalities by an amount that increases exponentially with N. These results are also robust against noise and perturbations of each observer's reference direction from the common direction.Comment: v2: Essentially published version (with typos fixed, results updated in Table 2 and Figure 4 replaced); v1: 16 pages, 5 figures, 2 tables, comments welcom

Reexamination of a multisetting Bell inequality for qudits

The class of d-setting, d-outcome Bell inequalities proposed by Ji and collaborators [Phys. Rev. A 78, 052103] are reexamined. For every positive integer d > 2, we show that the corresponding non-trivial Bell inequality for probabilities provides the maximum classical winning probability of the Clauser-Horne-Shimony-Holt-like game with d inputs and d outputs. We also demonstrate that the general classical upper bounds given by Ji et al. are underestimated, which invalidates many of the corresponding correlation inequalities presented thereof. We remedy this problem, partially, by providing the actual classical upper bound for d less than or equal to 13 (including non-prime values of d). We further determine that for prime value d in this range, most of these probability and correlation inequalities are tight, i.e., facet-inducing for the respective classical correlation polytope. Stronger lower and upper bounds on the quantum violation of these inequalities are obtained. In particular, we prove that once the probability inequalities are given, their correlation counterparts given by Ji and co-workers are no longer relevant in terms of detecting the entanglement of a quantum state.Comment: v3: Published version (minor rewordings, typos corrected, upper bounds in Table III improved/corrected); v2: 7 pages, 1 figure, 4 tables (substantially revised with new results on the tightness of the correlation inequalities included); v1: 7.5 pages, 1 figure, 4 tables (Comments are welcome

Inference of population splits and mixtures from genome-wide allele frequency data

Many aspects of the historical relationships between populations in a species are reflected in genetic data. Inferring these relationships from genetic data, however, remains a challenging task. In this paper, we present a statistical model for inferring the patterns of population splits and mixtures in multiple populations. In this model, the sampled populations in a species are related to their common ancestor through a graph of ancestral populations. Using genome-wide allele frequency data and a Gaussian approximation to genetic drift, we infer the structure of this graph. We applied this method to a set of 55 human populations and a set of 82 dog breeds and wild canids. In both species, we show that a simple bifurcating tree does not fully describe the data; in contrast, we infer many migration events. While some of the migration events that we find have been detected previously, many have not. For example, in the human data we infer that Cambodians trace approximately 16% of their ancestry to a population ancestral to other extant East Asian populations. In the dog data, we infer that both the boxer and basenji trace a considerable fraction of their ancestry (9% and 25%, respectively) to wolves subsequent to domestication, and that East Asian toy breeds (the Shih Tzu and the Pekingese) result from admixture between modern toy breeds and "ancient" Asian breeds. Software implementing the model described here, called TreeMix, is available at http://treemix.googlecode.comComment: 28 pages, 6 figures in main text. Attached supplement is 22 pages, 15 figures. This is an updated version of the preprint available at http://precedings.nature.com/documents/6956/version/

Three-dimensionality of space and the quantum bit: an information-theoretic approach

It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry "minimal amounts of direction information", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.Comment: 13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39

Device-independent quantum key distribution secure against collective attacks

Device-independent quantum key distribution (DIQKD) represents a relaxation of the security assumptions made in usual quantum key distribution (QKD). As in usual QKD, the security of DIQKD follows from the laws of quantum physics, but contrary to usual QKD, it does not rely on any assumptions about the internal working of the quantum devices used in the protocol. We present here in detail the security proof for a DIQKD protocol introduced in [Phys. Rev. Lett. 98, 230501 (2008)]. This proof exploits the full structure of quantum theory (as opposed to other proofs that exploit the no-signalling principle only), but only holds again collective attacks, where the eavesdropper is assumed to act on the quantum systems of the honest parties independently and identically at each round of the protocol (although she can act coherently on her systems at any time). The security of any DIQKD protocol necessarily relies on the violation of a Bell inequality. We discuss the issue of loopholes in Bell experiments in this context.Comment: 25 pages, 3 figure

Changed activation, oxygenation, and pain response of chronically painful muscles to repetitive work after training interventions: a randomized controlled trial

The aim of this randomized controlled trial was to assess changes in myalgic trapezius activation, muscle oxygenation, and pain intensity during repetitive and stressful work tasks in response to 10 weeks of training. In total, 39 women with a clinical diagnosis of trapezius myalgia were randomly assigned to: (1) general fitness training performed as leg-bicycling (GFT); (2) specific strength training of the neck/shoulder muscles (SST) or (3) reference intervention without physical exercise. Electromyographic activity (EMG), tissue oxygenation (near infrared spectroscopy), and pain intensity were measured in trapezius during pegboard and stress tasks before and after the intervention period. During the pegboard task, GFT improved trapezius oxygenation from a relative decrease of −0.83 ± 1.48 μM to an increase of 0.05 ± 1.32 μM, and decreased pain development by 43%, but did not affect resting levels of pain. SST lowered the relative EMG amplitude by 36%, and decreased pain during resting and working conditions by 52 and 38%, respectively, without affecting trapezius oxygenation. In conclusion, GFT performed as leg-bicycling decreased pain development during repetitive work tasks, possibly due to improved oxygenation of the painful muscles. SST lowered the overall level of pain both during rest and work, possibly due to a lowered relative exposure as evidenced by a lowered relative EMG. The results demonstrate differential adaptive mechanisms of contrasting physical exercise interventions on chronic muscle pain at rest and during repetitive work tasks

Measuring Measurement: Theory and Practice

Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well specified assumptions. The formalism is completely general and can be applied to a wide range of detectorsComment: 22 pages, 27 figure

A new interpretation of total column BrO during Arctic spring

Emission of bromine from sea-salt aerosol, frost flowers, ice leads, and snow results in the nearly complete removal of surface ozone during Arctic spring. Regions of enhanced total column BrO observed by satellites have traditionally been associated with these emissions. However, airborne measurements of BrO and O3 within the convective boundary layer (CBL) during the ARCTAS and ARCPAC field campaigns at times bear little relation to enhanced column BrO. We show that the locations of numerous satellite BrO "hotspots" during Arctic spring are consistent with observations of total column ozone and tropopause height, suggesting a stratospheric origin to these regions of elevated BrO. Tropospheric enhancements of BrO large enough to affect the column abundance are also observed, with important contributions originating from above the CBL. Closure of the budget for total column BrO, albeit with significant uncertainty, is achieved by summing observed tropospheric partial columns with calculated stratospheric partial columns provided that natural, short-lived biogenic bromocarbons supply between 5 and 10 ppt of bromine to the Arctic lowermost stratosphere. Proper understanding of bromine and its effects on atmospheric composition requires accurate treatment of geographic variations in column BrO originating from both the stratosphere and troposphere. Copyright 2010 by the American Geophysical Union

Likely country of origin in publications on randomised controlled trials and controlled clinical trials during the last 60 years

BACKGROUND: The number of publications on clinical trials is unknown as well as the countries publishing most trial reports. To try to examine these questions we performed an ecological study. METHODS: We searched the 454,449 records on publications in The Cochrane Central Register of Controlled Trials (CENTRAL) in The Cochrane Library, Issue 3, 2005 (CD-ROM version) for possible country of origin. We inspected a random sample of 906 records for information on country and type of trial. RESULTS: There was an exponential growth of publications on randomised controlled trials and controlled clinical trials since 1946, but the growth seems to have seized since 2000. We identified the possible country of origin of 210,974 publications (46.4%). The USA is leading with about 46,789 publications followed by UK, Germany, Italy, the Netherlands, Canada, and France. Sweden becomes the leader with 891 publications per million inhabitants during the last 60 years followed by Denmark (n = 864), New Zealand (n = 791), Finland (n = 781), the Netherlands (n = 570), Switzerland (n = 547), and Norway (n = 543). In depth assessment of the random sample backed these findings. CONCLUSION: Many records lacked country of origin, even after the additional scrutiny. The number of publications on clinical trials increased exponentially until the turn of the century. Rather small, democratic, and wealthy countries take the lead when the number of publications on clinical trials is calculated based on million inhabitants. If all countries produced the same number of trials as these countries, this could mean thousands of new effective treatments during the next 60 years