Two-dimensional simply connected abelian locally Nash groups

The aim of this paper is to give a description of simply connected abelian locally Nash groups of dimension $2$. Along the way we prove that, for any $n\geq 2$, a locally Nash structure over $(\mathbb{R}^n,+)$ can be characterized via a meromorphic map admitting an algebraic addition theorem.Comment: The results of this paper have been polished and extended. They appear in arXiv:1704.08514, arXiv:1707.08171 and arXiv:1711.0080

The maximally entangled set of 4-qubit states

Entanglement is a resource to overcome the natural restriction of operations used for state manipulation to Local Operations assisted by Classical Communication (LOCC). Hence, a bipartite maximally entangled state is a state which can be transformed deterministically into any other state via LOCC. In the multipartite setting no such state exists. There, rather a whole set, the Maximally Entangled Set of states (MES), which we recently introduced, is required. This set has on the one hand the property that any state outside of this set can be obtained via LOCC from one of the states within the set and on the other hand, no state in the set can be obtained from any other state via LOCC. Recently, we studied LOCC transformations among pure multipartite states and derived the MES for 3- and generic 4-qubit states. Here, we consider the non-generic 4-qubit states and analyze their properties regarding local transformations. We prove that most SLOCC classes show a similar behavior as the generic states, however we also identify three classes with very distinct properties. The first consists of the GHZ and W class, where any state can be transformed into some other state non-trivially. In particular, there exists no isolation. On the other hand, there also exist classes where all states are isolated. Last but not least we identify an additional class of states, whose transformation properties differ drastically from all the other classes. Our investigations do not only identify the most relevant classes of states for LOCC entanglement manipulation, but also reveal new insight into the similarities and differences between separable and LOCC transformations and enable the investigation of LOCC transformations among arbitrary four qubit states.Comment: 68 pages (including appendix), minor change

Remote entanglement preparation

We introduce a new multipartite communication scheme, with the aim to enable the senders to remotely and obliviously provide the receivers with an arbitrary amount of multipartite entanglement. The scheme is similar to Remote State Preparation (RSP). However, we show that even though the receivers are restricted to local unitary operations, the required resources for remote entanglement preparation are less than for RSP. In order to do so we introduce a novel canonical form of arbitrary multipartite pure states describing an arbitrary number of qubits. Moreover, we show that if the receivers are enabled to perform arbitrary local operations and classical communication, the required resources can drastically be reduced. We employ this protocol to derive robust entanglement purification protocols for arbitrary pure states and show that it can also be used for sending classical information.Comment: 8 pages (including appendix), 3 figures; replaced with published versio

The ionized gas in the Galactic Center Radio Arc

We present Infrared Space Observatory (ISO) observations of fine structure lines toward the Radio Arc region, close to Sgr A, in the Galactic center region (GCR). The ionization at large scale is dominated by the clusters of massive stars in this region: the Quintuplet and the Arches cluster. Any other possible mechanism as interaction with the magnetic fields revealed by the Non-Thermal Filaments (NTFs) must play a minor role. The radiation in this area is relatively hard ($T_\mathrm{eff}\sim 33-35$ kK) but diluted. It reaches large distances due to the inhomogeneity of the medium.Comment: 2 pages, 2 figures. Contribution to the conference "The evolution of galaxies II: basic building blocks", Eds. Sauvage, Vigroux, Schaerer, Madden, Use kluwer.cl

Extraction of nucleon axial charge and radius from lattice QCD results using baryon chiral perturbation theory

We calculate the nucleon axial form factor up to the leading one-loop order in a covariant chiral effective field theory with the $\Delta(1232)$ resonance as an explicit degree of freedom. We fit the axial form factor to the latest lattice QCD data and pin down the relevant low-energy constants. The lattice QCD data, for various pion masses below $400$ MeV, can be well described up to a momentum transfer of $\sim 0.6$ GeV. The $\Delta(1232)$ loops contribute significantly to this agreement. Furthermore, we extract the axial charge and radius based on the fitted values of the low energy constants. The results are: $g_A=1.237(74)$ and $\langle r_A^2\rangle =0.263(38)~{\rm fm}^2$. The obtained coupling $g_A$ is consistent with the experimental value if the uncertainty is taken into account. The axial radius is below but in agreement with the recent extraction from neutrino quasi-elastic scattering data on deuterium, which has large error bars. Up to our current working accuracy, $r_A$ is predicted only at leading order, i.e., one-loop level. A more precise determination might need terms of $\mathcal{O}(p^5)$.Comment: Published versio

Complete set of operational measures for the characterization of 3-qubit entanglement

We characterize the entanglement contained in a pure three-qubit state via operational entanglement measures. To this end we derive a new decomposition for arbitrary 3-qubit states which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities measure on the one hand the entanglement required to generate the state and on the other hand the entanglement contained in the state and have a clear physical meaning. Moreover, we show that the classification of states obtained in this way is strongly related to the one obtained when considering general local operations and classical communication.Comment: 11 pages (including appendix), 1 figure; replaced with published versio

Entangled pure state transformations via local operations assisted by finitely many rounds of classical communication

We consider generic pure $n$-qubit states and a general class of pure states of arbitrary dimensions and arbitrarily many subsystems. We characterize those states which can be reached from some other state via Local Operations assisted by finitely many rounds of Classical Communication ($LOCC_{\mathbb{N}}$). For $n$ qubits with $n>3$ we show that this set of states is of measure zero, which implies that the maximally entangled set is generically of full measure if restricted to the practical scenario of $LOCC_{\mathbb{N}}$. Moreover, we identify a class of states for which any $LOCC_{\mathbb{N}}$ protocol can be realized via a concatenation of deterministic steps. We show, however, that in general there exist state transformations which require a probabilistic step within the protocol, which highlights the difference between bipartite and multipartite LOCC.Comment: 5 pages, 1 figure. See also the companion paper arXiv:1607.0514

Entanglement manipulation of multipartite pure states with finite rounds of classical communication

We studied pure state transformations using local operations assisted by finitely many rounds of classical communication ($LOCC_{\mathbb{N}}$) in C. Spee, J.I. de Vicente, D. Sauerwein, B. Kraus, arXiv:1606.04418 (2016). Here, we first of all present the details of some of the proofs and generalize the construction of examples of state transformations via $LOCC_{\mathbb{N}}$ which require a probabilistic step. However, we also present explicit examples of SLOCC classes where any separable transformation can be realized by a protocol in which each step is deterministic (all-det-$LOCC_{\mathbb{N}}$). Such transformations can be considered as natural generalizations of bipartite transformations. Furthermore, we provide examples of pure state transformations which are possible via separable transformations, but not via $LOCC_{\mathbb{N}}$. We also analyze an interesting genuinely multipartite effect which we call locking or unlocking the power of other parties. This means that one party can prevent or enable the implementation of LOCC transformations by other parties. Moreover, we investigate the maximally entangled set restricted to $LOCC_{\mathbb{N}}$ and show how easily computable bounds on some entanglement measures can be derived by restricting to $LOCC_{\mathbb{N}}$.Comment: 19 pages, 3 figures. See also the companion paper arXiv:1606.0441

Automatic unsupervised classification of all SDSS/DR7 galaxy spectra

Using the 'k-means' cluster analysis algorithm, we carry out an unsupervised classification of all galaxy spectra in the seventh and final Sloan Digital Sky Survey data release (SDSS/DR7). Except for the shift to restframe wavelengths, and the normalization to the g-band flux, no manipulation is applied to the original spectra. The algorithm guarantees that galaxies with similar spectra belong to the same class. We find that 99 % of the galaxies can be assigned to only 17 major classes, with 11 additional minor classes including the remaining 1%. The classification is not unique since many galaxies appear in between classes, however, our rendering of the algorithm overcomes this weakness with a tool to identify borderline galaxies. Each class is characterized by a template spectrum, which is the average of all the spectra of the galaxies in the class. These low noise template spectra vary smoothly and continuously along a sequence labeled from 0 to 27, from the reddest class to the bluest class. Our Automatic Spectroscopic K-means-based (ASK) classification separates galaxies in colors, with classes characteristic of the red sequence, the blue cloud, as well as the green valley. When red sequence galaxies and green valley galaxies present emission lines, they are characteristic of AGN activity. Blue galaxy classes have emission lines corresponding to star formation regions. We find the expected correlation between spectroscopic class and Hubble type, but this relationship exhibits a high intrinsic scatter. Several potential uses of the ASK classification are identified and sketched, including fast determination of physical properties by interpolation, classes as templates in redshift determinations, and target selection in follow-up works (we find classes of Seyfert galaxies, green valley galaxies, as well as a significant number of outliers). The ASK classification is publicly accessible through various websites.Comment: Accepted for publication in ApJ. 15 figs. 20 pages. Free classification @ ftp://ask:[email protected]

On the robustness of the pendulum model for large-amplitude longitudinal oscillations in prominences

Large-amplitude longitudinal oscillations (LALOs) in prominences are spectacular manifestations of the solar activity. In such events nearby energetic disturbances induce periodic motions on filaments with displacements comparable to the size of the filaments themselves and with velocities larger than 20 km/s. The pendulum model, in which the gravity projected along a rigid magnetic field is the restoring force, was proposed to explain these events. However, it can be objected that in a realistic situation where the magnetic field reacts to the mass motion of the heavy prominence, the simplified pendulum model could be no longer valid. We have performed non-linear time-dependent numerical simulations of LALOs considering a dipped magnetic field line structure. In this work we demonstrate that for even relatively weak magnetic fields the pendulum model works very well. We therefore validate the pendulum model and show its robustness, with important implications for prominence seismology purposes. With this model it is possible to infer the geometry of the dipped field lines that support the prominence.Comment: Accepted for publication in The Astrophysical Journa