A composite parameterization of unitary groups, density matrices and subspaces

Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group $\mathcal{U}(d)$ of arbitrary dimension $d$ which is constructed in a composite way. We show explicitly how any element of $\mathcal{U}(d)$ can be composed of matrix exponential functions of generalized anti-symmetric $\sigma$-matrices and one-dimensional projectors. The specific form makes it considerably easy to identify and discard redundant parameters in several cases. In this way, redundancy-free density matrices of arbitrary rank $k$ can be formulated. Our construction can also be used to derive an orthonormal basis of any $k$-dimensional subspaces of $\mathbb{C}^d$ with the minimal number of parameters. As an example it will be shown that this feature leads to a significant reduction of parameters in the case of investigating distillability of quantum states via lower bounds of an entanglement measure (the $m$-concurrence).Comment: 13 pages, 1 figur

Lorentz invariance of entanglement classes in multipartite systems

We analyze multipartite entanglement in systems of spin-1/2 particles from a relativistic perspective. General conditions which have to be met for any classification of multipartite entanglement to be Lorentz invariant are derived, which contributes to a physical understanding of entanglement classification. We show that quantum information in a relativistic setting requires the partition of the Hilbert space into particles to be taken seriously. Furthermore, we study exemplary cases and show how the spin and momentum entanglement transforms relativistically in a multipartite setting.Comment: v2: 5 pages, 4 figures, minor changes to main body, journal references update

The potential of artificial aging for modelling of natural aging processes of ballpoint ink

Artificial aging has been used to reproduce natural aging processes in an accelerated pace. Questioned documents were exposed to light or high temperature in a well-defined manner in order to simulate an increased age. This may be used to study the aging processes or to date documents by reproducing their aging curve. Ink was studied especially because it is deposited on the paper when a document, such as a contract, is produced. Once on the paper, aging processes start through degradation of dyes, solvents drying and resins polymerisation. Modelling of dye's and solvent's aging was attempted. These processes, however, follow complex pathways, influenced by many factors which can be classified as three major groups: ink composition, paper type and storage conditions. The influence of these factors is such that different aging states can be obtained for an identical point in time. Storage conditions in particular are difficult to simulate, as they are dependent on environmental conditions (e.g. intensity and dose of light, temperature, air flow, humidity) and cannot be controlled in the natural aging of questioned documents. The problem therefore lies more in the variety of different conditions a questioned document might be exposed to during its natural aging, rather than in the simulation of such conditions in the laboratory. Nevertheless, a precise modelling of natural aging curves based on artificial aging curves is obtained when performed on the same paper and ink. A standard model for aging processes of ink on paper is therefore presented that is based on a fit of aging curves to a power law of solvent concentrations as a function of time. A mathematical transformation of artificial aging curves into modelled natural aging curves results in excellent overlap with data from real natural aging processes

A simplex of bound entangled multipartite qubit states

We construct a simplex for multipartite qubit states of even number n of qubits, which has the same geometry concerning separability, mixedness, kind of entanglement, amount of entanglement and nonlocality as the bipartite qubit states. We derive the entanglement of the class of states which can be described by only three real parameters with the help of a multipartite measure for all discrete systems. We prove that the bounds on this measure are optimal for the whole class of states and that it reveals that the states possess only n-partite entanglement and not e.g. bipartite entanglement. We then show that this n-partite entanglement can be increased by stochastic local operations and classical communication to the purest maximal entangled states. However, pure n-partite entanglement cannot be distilled, consequently all entangled states in the simplex are n-partite bound entangled. We study also Bell inequalities and find the same geometry as for bipartite qubits. Moreover, we show how the (hidden) nonlocality for all n-partite bound entangled states can be revealed.Comment: 11 pages, 4 figures; 2nd version changed considerably and a detailed derivation of the multipartite measure is include

Experimentally implementable criteria revealing substructures of genuine multipartite entanglement

We present a general framework that reveals substructures of genuine multipartite entanglement. Via simple inequalities it is possible to discriminate different sets of multipartite qubit states. These inequalities are beneficial regarding experimental examinations as only local measurements are required. Furthermore, the number of observables scales favorably with system size. In exemplary cases we demonstrate the noise resistance and discuss implementations.Comment: 14 pages, 4 figure

Comparison of performance and fitness traits in German Angler, Swedish Red and Swedish Polled with Holstein dairy cattle breeds under organic production

Although the use of local breeds is recommended by organic regulations, breed comparisons performed under organic production conditions with similar production intensities are scarce. Therefore, we compared data of local and widely used Holstein dairy cattle breeds from 2011 to 2015 regarding production, fertility and health from German and Swedish organic farms with similar management intensities within country. In Germany, the energy-corrected total milk yield tended to be lower in the local breed Original Angler Cattle (AAZ, 5193 kg) compared to the modern German Holstein Friesian breed (HO, 5620 kg), but AAZ showed higher milk fat and protein contents (AAZ v. HO: 5.09% v. 4.18% and 3.61% v. 3.31%, respectively). In Sweden, the widely used modern Swedish Holstein (SH) breed had the highest milk yield (9209 kg, fat: 4.10%, protein: 3.31%), while the local Swedish Polled (SKB) showed highest milk yield, fat and protein contents (6169 kg, 4.47%, 3.50%, respectively), followed by the local breed Swedish Red (SRB, 8283 kg, 4.33%, 3.46%, respectively). With regard to fertility characteristics, the German breeds showed no differences, but AAZ tended to have less days open compared to HO (−17 days). In Sweden, breeds did not differ with regard to calving interval, but both local breeds showed a lower number of days open (−10.4 in SRB and −24.1 in SKB compared to SH), and SKB needed fewer inseminations until conception (−0.5 inseminations) compared to SH. Proportion of test day records with a somatic cell count content of ≥100 000 cells per ml milk did not reveal breed differences in any of the two countries. German breeds did not differ regarding the proportion of cows with veterinary treatments. In Sweden, SRB showed the lowest proportion of cows with general veterinary treatment as well as specific treatment due to udder problems (22.8 ± 6.42 and 8.05 ± 2.18, respectively), but the local breed SKB did not differ from SH in either of the two traits. In Sweden, we found no breed differences regarding veterinary treatments due to fertility problems or diagnosis of claw or leg problems during claw trimming. Our results indicate a stronger expression of the antagonism between production and functional traits with increasing production intensity. Future breed comparisons, therefore, need to consider different production intensities within organic farming in order to derive practical recommendations as to how to implement European organic regulations with regard to a suitable choice of breeds

Expiratory muscle fatigue impairs exercise performance

High-intensity, exhaustive exercise may lead to inspiratory as well as expiratory muscle fatigue (EMF). Induction of inspiratory muscle fatigue (IMF) before exercise has been shown to impair subsequent exercise performance. The purpose of the present study was to determine whether induction of EMF also affects subsequent exercise performance. Twelve healthy young men performed five 12-min running tests on a 400-m track on separate days: a preliminary trial, two trials after induction of EMF, and two trials without prior muscle fatigue. Tests with and without prior EMF were performed in an alternate order, randomly starting with either type. EMF was defined as a ≥20% drop in maximal expiratory mouth pressure achieved during expiratory resistive breathing against 50% maximal expiratory mouth pressure. The average distance covered in 12min was significantly smaller during exercise with prior EMF compared to control exercise (2872±256 vs. 2957±325m; P=0.002). Running speed was consistently lower (0.13ms−1) throughout the entire 12min of exercise with prior EMF. A significant correlation was observed between the level of EMF (decrement in maximal expiratory mouth pressure after resistive breathing) and the reduction in running distance (r 2=0.528, P=0.007). Perceived respiratory exertion was higher during the first 800m and heart rate was lower throughout the entire test of running with prior EMF compared to control exercise (5.3±1.6 vs. 4.5±1.7 points, P=0.002; 173±10 vs. 178±7beatsmin−1, P=0.005). We conclude that EMF impairs exercise performance as previously reported for IM