SLOCC invariant and semi-invariants for SLOCC classification of four-qubits

We show there are at least 28 distinct true SLOCC entanglement classes for four-qubits by means of SLOCC invariant and semi-invariants and derive the number of the degenerated SLOCC classes for n-qubits.Comment: 22 pages, no figures, 9 tables, submit the paper to a journa

Phase space spinor amplitudes for spin 1/2 systems

The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-\half is treated in detail, and it is shown that phase space amplitudes on the sphere transform correctly as spinors under under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-\half magnetic dipole in a time-dependent magnetic field.Comment: 19 pages, added new results, fixed typo

Derivatives of spin dynamics simulations

We report analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters. The methods described are significantly faster, more accurate and more reliable than the finite difference approximations typically employed. The resulting derivatives may be used in fitting, optimization, performance evaluation and stability analysis of spin dynamics simulations and experiments. Keywords: NMR, EPR, simulation, analytical derivatives, optimal control, spin chemistry, radical pair.Comment: Accepted by The Journal of Chemical Physic

Twitter Use and its Effects on Student Perception of Instructor Credibility

This study investigates college student perceptions of instructor credibility based on the content of an instructor’s Twitterfeed and student beliefs about Twitter as a communication tool. Quantitative and qualitative methods were utilized to explore the effects of three manipulated Twitter feeds (e.g., tweeting social topics, professional topics, or a blend) on student perceptions of instructor credibility and examine how students perceive Twitter as a teaching tool. Quantitative results suggest that the profile with professional content was most credible. Credibility ratings were also associated with other Twitter use variables, including positive student attitudes about instructors who use Twitter and Tweet frequency. Coded qualitative responses indicated that Twitter may be both an asset and an obstacle for instructors

Channel kets, entangled states, and the location of quantum information

The well-known duality relating entangled states and noisy quantum channels is expressed in terms of a channel ket, a pure state on a suitable tripartite system, which functions as a pre-probability allowing the calculation of statistical correlations between, for example, the entrance and exit of a channel, once a framework has been chosen so as to allow a consistent set of probabilities. In each framework the standard notions of ordinary (classical) information theory apply, and it makes sense to ask whether information of a particular sort about one system is or is not present in another system. Quantum effects arise when a single pre-probability is used to compute statistical correlations in different incompatible frameworks, and various constraints on the presence and absence of different kinds of information are expressed in a set of all-or-nothing theorems which generalize or give a precise meaning to the concept of ``no-cloning.'' These theorems are used to discuss: the location of information in quantum channels modeled using a mixed-state environment; the $CQ$ (classical-quantum) channels introduced by Holevo; and the location of information in the physical carriers of a quantum code. It is proposed that both channel and entanglement problems be classified in terms of pure states (functioning as pre-probabilities) on systems of $p\geq 2$ parts, with mixed bipartite entanglement and simple noisy channels belonging to the category $p=3$, a five-qubit code to the category $p=6$, etc.; then by the dimensions of the Hilbert spaces of the component parts, along with other criteria yet to be determined.Comment: Latex 32 pages, 4 figures in text using PSTricks. Version 3: Minor typographical errors correcte

The 1600 CE Huaynaputina eruption as a possible trigger for persistent cooling in the North Atlantic region

Paleoclimate reconstructions have identified a period of exceptional summer and winter cooling in the North Atlantic region following the eruption of the tropical volcano Huaynaputina (Peru) in 1600 CE. A previous study based on numerical climate simulations has indicated a potential mechanism for the persistent cooling in a slowdown of the North Atlantic subpolar gyre (SPG) and consequent ocean-atmosphere feedbacks. To examine whether this mechanism could have been triggered by the Huaynaputina eruption, this study compares the simulations used in the previous study both with and without volcanic forcing and this SPG shift to reconstructions from annual proxies in natural archives and historical written records as well as contemporary historical observations of relevant climate and environmental conditions. These reconstructions and observations demonstrate patterns of cooling and sea-ice expansion consistent with, but not indicative of, an eruption trigger for the proposed SPG slowdown mechanism. The results point to possible improvements in future model-data comparison studies utilizing historical written records. Moreover, we consider historical societal impacts and adaptations associated with the reconstructed climatic and environmental anomalies

Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals

Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often in experimental condensed-matter physics and materials engineering as data. These predictions are used to analyze recent measurements, or to plan future experiments. Increasingly more experimental scientists in these fields therefore face the natural question: what is the expected error for such an ab initio prediction? Information and experience about this question is scattered over two decades of literature. The present review aims to summarize and quantify this implicit knowledge. This leads to a practical protocol that allows any scientist - experimental or theoretical - to determine justifiable error estimates for many basic property predictions, without having to perform additional DFT calculations. A central role is played by a large and diverse test set of crystalline solids, containing all ground-state elemental crystals (except most lanthanides). For several properties of each crystal, the difference between DFT results and experimental values is assessed. We discuss trends in these deviations and review explanations suggested in the literature. A prerequisite for such an error analysis is that different implementations of the same first-principles formalism provide the same predictions. Therefore, the reproducibility of predictions across several mainstream methods and codes is discussed too. A quality factor Delta expresses the spread in predictions from two distinct DFT implementations by a single number. To compare the PAW method to the highly accurate APW+lo approach, a code assessment of VASP and GPAW with respect to WIEN2k yields Delta values of 1.9 and 3.3 meV/atom, respectively. These differences are an order of magnitude smaller than the typical difference with experiment, and therefore predictions by APW+lo and PAW are for practical purposes identical.Comment: 27 pages, 20 figures, supplementary material available (v5 contains updated supplementary material

A non-autonomous stochastic discrete time system with uniform disturbances

The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is proved that the Bayes control for the Pareto priors is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. These results are extended to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of these type of systems are non-square matrices. The paper extends the results of the authors developed for system with disturbances belonging to the exponential family

Minimum Decision Cost for Quantum Ensembles

For a given ensemble of $N$ independent and identically prepared particles, we calculate the binary decision costs of different strategies for measurement of polarised spin 1/2 particles. The result proves that, for any given values of the prior probabilities and any number of constituent particles, the cost for a combined measurement is always less than or equal to that for any combination of separate measurements upon sub-ensembles. The Bayes cost, which is that associated with the optimal strategy (i.e., a combined measurement) is obtained in a simple closed form.Comment: 11 pages, uses RevTe

Galaxy Merger Candidates in High-Redshift Cluster Environments

We compile a sample of spectroscopically- and photometrically-selected cluster galaxies from four high-redshift galaxy clusters ($1.59 < z < 1.71$) from the Spitzer Adaptation of the Red-Sequence Cluster Survey (SpARCS), and a comparison field sample selected from the UKIDSS Deep Survey. Using near-infrared imaging from the \textit{Hubble Space Telescope} we classify potential mergers involving massive ($M_* \geq 3\times 10^{10}\mathrm{M}_\odot$) cluster members by eye, based on morphological properties such as tidal distortions, double nuclei, and projected near neighbors within 20 kpc. With a catalogue of 23 spectroscopic and 32 photometric massive cluster members across the four clusters and 65 spectroscopic and 26 photometric comparable field galaxies, we find that after taking into account contamination from interlopers, $11.0 ^{+7.0}_{-5.6}\%$ of the cluster members are involved in potential mergers, compared to $24.7^{+5.3}_{-4.6}\%$ of the field galaxies. We see no evidence of merger enhancement in the central cluster environment with respect to the field, suggesting that galaxy-galaxy merging is not a stronger source of galaxy evolution in cluster environments compared to the field at these redshifts.Comment: Accepted by Ap