Conditional q-Entropies and Quantum Separability: A Numerical Exploration

We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's and Tsallis' measures constitute particular instances of these entropies. We perform a systematic numerical survey of the space of mixed states of two-qubit systems in order to determine, as a function of the degree of mixture, and for different values of the entropic parameter q, the volume in state space occupied by those states characterized by positive values of the relative entropy. Similar calculations are performed for qubit-qutrit systems and for composite systems described by Hilbert spaces of larger dimensionality. We pay particular attention to the limit case q --> infinity. Our numerical results indicate that, as the dimensionalities of both subsystems increase, composite quantum systems tend, as far as their relative q-entropies are concerned, to behave in a classical way

Entanglement Distribution and Entangling Power of Quantum Gates

Quantum gates, that play a fundamental role in quantum computation and other quantum information processes, are unitary evolution operators $\hat U$ that act on a composite system changing its entanglement. In the present contribution we study some aspects of these entanglement changes. By recourse of a Monte Carlo procedure, we compute the so called "entangling power" for several paradigmatic quantum gates and discuss results concerning the action of the CNOT gate. We pay special attention to the distribution of entanglement among the several parties involved

Induced measures in the space of mixed quantum states

We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a N x K composite system, induces a unique measure in the space of N x N mixed states (or in the space of K x K mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of $N \times N$ pure states behaves as lnN-1/2.Comment: 12 latex pages, 2 figures in epsf, submited to J. Phys. A. ver.3, some improvements and a few references adde

Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems

We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized volume elements of the Bures (minimal monotone) metric for n = 2 and 3, obtaining thereby "Bures prior probability distributions" over the two- and three-state systems. Then, as an essential first step in extending these results to n > 3, we determine that the "Hall normalization constant" (C_{n}) for the marginal Bures prior probability distribution over the (n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known to equal 2/pi.) The constant C_{5} is also found. It too is associated with a remarkably simple decompositon, involving the product of the eight consecutive prime numbers from 2 to 23. We also preliminarily investigate several cases, n > 5, with the use of quasi-Monte Carlo integration. We hope that the various analyses reported will prove useful in deriving a general formula (which evidence suggests will involve the Bernoulli numbers) for the Hall normalization constant for arbitrary n. This would have diverse applications, including quantum inference and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in J. Phys. A. We make a few slight changes from the previous version, but also add a subsection (III G) in which several variations of the basic problem are newly studied. Rather strong evidence is adduced that the Hall constants are related to partial sums of denominators of the even-indexed Bernoulli numbers, although a general formula is still lackin

Global Wheat Head Detection (GWHD) dataset: a large and diverse dataset of high resolution RGB labelled images to develop and benchmark wheat head detection methods

Detection of wheat heads is an important task allowing to estimate pertinent traits including head population density and head characteristics such as sanitary state, size, maturity stage and the presence of awns. Several studies developed methods for wheat head detection from high-resolution RGB imagery. They are based on computer vision and machine learning and are generally calibrated and validated on limited datasets. However, variability in observational conditions, genotypic differences, development stages, head orientation represents a challenge in computer vision. Further, possible blurring due to motion or wind and overlap between heads for dense populations make this task even more complex. Through a joint international collaborative effort, we have built a large, diverse and well-labelled dataset, the Global Wheat Head detection (GWHD) dataset. It contains 4,700 high-resolution RGB images and 190,000 labelled wheat heads collected from several countries around the world at different growth stages with a wide range of genotypes. Guidelines for image acquisition, associating minimum metadata to respect FAIR principles and consistent head labelling methods are proposed when developing new head detection datasets. The GWHD is publicly available at http://www.global-wheat.com/ and aimed at developing and benchmarking methods for wheat head detection.Comment: 16 pages, 7 figures, Dataset pape

A roadmap for gene functional characterisation in wheat

To adapt to the challenges of climate change and the growing world population, it is vital to increase global crop production. Understanding the function of genes within staple crops will accelerate crop improvement by allowing targeted breeding approaches. Despite the importance of wheat, which provides 20 % of the calories consumed by humankind, a lack of genomic information and resources has hindered the functional characterisation of genes in this species. The recent release of a high-quality reference sequence for wheat underpins a suite of genetic and genomic resources that support basic research and breeding. These include accurate gene model annotations, gene expression atlases and gene networks that provide background information about putative gene function. In parallel, sequenced mutation populations, improved transformation protocols and structured natural populations provide rapid methods to study gene function directly. We highlight a case study exemplifying how to integrate these resources to study gene function in wheat and thereby accelerate improvement in this important crop. We hope that this review provides a helpful guide for plant scientists, especially those expanding into wheat research for the first time, to capitalise on the discoveries made in Arabidopsis and other plants. This will accelerate the improvement of wheat, a complex polyploid crop, of vital importance for food and nutrition security

Long-term CD4+ T-cell count evolution after switching from regimens including HIV nucleoside reverse transcriptase inhibitors (NRTI) plus protease inhibitors to regimens containing NRTI plus non-NRTI or only NRTI

BACKGROUND: Data regarding CD4+ recovery after switching from protease inhibitor (PI)-based regimens to regimens not containing PI are scarce. METHODS: Subjects with virological success on first-PI-regimens who switched to NNRTI therapy (NNRTI group) or to nucleoside reverse transcriptase (NRTI)-only (NRTI group) were studied. The effect of the switch on the ongoing CD4+ trend was assessed by two-phase linear regression (TPLR), allowing us to evaluate whether a change in the CD4+ trend (hinge) occurred and the time of its occurrence. Furthermore, we described the evolution of the frequencies in CD4-count classes across four relevant time-points (baseline, before and immediately after the switch, and last visit). Finally, we explored whether the CD4+ counts evolved differently in patients who switched to NNRTI or NRTI-only regimens by considering: the overall CD4+ trends, the time to CD4+ 65 500/mm3 after the switch, and the area-under-the-curve (AUC) of the CD4+ after the switch. RESULTS: Eight hundred and ninety-six patients, followed for a median of 2,121 days, were included. At TPLR, hinges occurred in 581/844 (68.9%), but in only 40/581 (6.9%) within a time interval (180 days) compatible with a possible relationship to the switch; furthermore, in 19/40 cases, CD4+ counts appeared to decrease after the hinges. In comparison with the NNRTI group, the NRTI group showed CD4+ count greater at baseline (P = 0.0234) and before the switch (P 64 0.0001), superior CD4+ T-cell increases after HAART was started, lower probability of not achieving CD4+ 65 500/mm3 (P = 0.0024), and, finally, no significant differences in the CD4+ T-cell AUC after the switch after adjusting for possible confounders (propensity score and pre-switch AUC). Persistence at CD4+ < 200/mm3 was observed in 34/435 (7.5%) patients, and a decrease below this level was found in only 10/259 (3.9%) with baseline CD4+ 65 350/mm3. CONCLUSIONS: Switching from first-line PI to NNRTI- or NRTI-based regimens did not seem to impair CD4+ trend over long-term follow-up. Although the greater CD4+ increases in patients who switched to the NRTI-only regimen was due to higher CD4+ counts before the switch, several statistical analyses consistently showed that switching to this regimen did not damage the ongoing immune-reconstitution. Lastly, the observation that CD4+ T-cell counts remained low or decreased in the long term despite virological success merits further investigation

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

First measurements of the performance of the Barrel RPC system in CMS

During the summer 2006, a first integrated test of a part of the CMS experiment was performed at CERN collecting a data sample of several millions of cosmic rays events. A fraction of the Resistive Plate Chambers system was successfully operated. Results on the RPC performance are reported