Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems

We seek to derive the probability--expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the partial transposes (PT's) of the associated 4 x 4 density matrices). But the full implementation of the test--requiring that the determinant of the PT be nonnegative for separability to hold--appears to be, at least presently, computationally intractable. So, we have previously implemented--using the auxiliary concept of a diagonal-entry-parameterized separability function (DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal minors of the PT. This yielded an exact upper bound on the separability probability of 1024/{135 pi^2} =0.76854$. Here, we piece together (reflection-symmetric) results obtained by requiring that each of the four 3 x 3 principal minors of the PT, in turn, be nonnegative, giving an improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a still further improved upper bound of 1129/2100 = 0.537619 can be found by similarly piecing together the (reflection-symmetric) results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors. In deriving our improved upper bounds, we rely repeatedly upon the use of certain integrals over cubes that arise. Finally, we apply an independence assumption to a pair of DESF's that comes close to reproducing our numerical estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the end are correcte

A priori probability that a qubit-qutrit pair is separable

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjecture

Alignments and misalignments of realized marketing strategies with administrative systems: Performance implications

On the basis of intended marketing strategy plans, firms design administrative systems to support strategy implementation. In increasingly turbulent business environments-characterized by complexity, scarce resources, and escalating competitive opportunities and threats-firms are forced to alter intended and realize emergent strategies more frequently than ever before. The eventualities of realized marketing strategies may lead to misalignments between the strategy and the existing administrative system designed to support it. To examine performance implications of such misalignments we use Slater and Olson's (2001) taxonomy of marketing strategies. We distinguish between intended and realized plans and we propose an administrative system framework of structural (i.e., centralization, formalization, and specialization) and dynamic (i.e., interdepartmental connectedness and strategic control mechanisms) parameters for the effective implementation of realized strategies. We propose three-way interactions between realized marketing strategies and the dynamic parameters of the system. Research hypotheses on performance implications and responses from 215 marketing executives show performance differences across strategy types and (mis)alignments of the administrative system. Our findings confirm three-way interactions among strategy types, interdepartmental connectedness, and control mechanisms for all realized strategy types

On the ab initio calculation of CVV Auger spectra in closed-shell systems

We propose an ab initio method to evaluate the core-valence-valence (CVV) Auger spectrum of systems with filled valence bands. The method is based on the Cini-Sawatzky theory, and aims at estimating the parameters by first-principles calculations in the framework of density-functional theory (DFT). Photoemission energies and the interaction energy for the two holes in the final state are evaluated by performing DFT simulations for the system with varied population of electronic levels. Transition matrix elements are taken from atomic results. The approach takes into account the non-sphericity of the density of states of the emitting atom, spin-orbit interaction in core and valence, and non quadratic terms in the total energy expansion with respect to fractional occupation numbers. It is tested on two benchmark systems, Zn and Cu metals, leading in both cases to L23M45M45 Auger peaks within 2 eV from the experimental ones. Detailed analysis is presented on the relative weight of the various contributions considered in our method, providing the basis for future development. Especially problematic is the evaluation of the hole-hole interaction for systems with broad valence bands: our method underestimates its value in Cu, while we obtain excellent results for this quantity in Zn.Comment: 20 pages, 5 figures, 4 table

Electron shielding of the nuclear magnetic moment in hydrogen-like atom

The correction to the wave function of the ground state in a hydrogen-like atom due to an external homogenous magnetic field is found exactly in the parameter $Z\alpha$. The $j=1/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the external homogeneous magnetic field is found for arbitrary $n$. The $j=3/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the nuclear magnetic moment is also found for arbitrary $n$. Using these results, we have calculated the shielding of the nuclear magnetic moment by the $ns_{1/2}$ electron.Comment: 15 page

Spin-dependent transport in molecular tunnel junctions

We present measurements of magnetic tunnel junctions made using a self-assembled-monolayer molecular barrier. Ni/octanethiol/Ni samples were fabricated in a nanopore geometry. The devices exhibit significant changes in resistance as the angle between the magnetic moments in the two electrodes is varied, demonstrating that low-energy electrons can traverse the molecular barrier while maintaining spin coherence. An analysis of the voltage and temperature dependence of the data suggests that the spin-coherent transport signals can be degraded by localized states in the molecular barriers.Comment: 4 pages, 5 color figure

The value-added of primary schools: what is it really measuring?

This paper compares the official value-added scores in 2005 for all primary schools in three adjacent LEAs in England with the raw-score Key Stage 2 results for the same schools. The correlation coefficient for the raw- and value-added scores of these 457 schools is around +0.75. Scatterplots show that there are no low attaining schools with average or higher value-added, and no high attaining schools with below average value-added. At least some of the remaining scatter is explained by the small size of some schools. Although some relationship between these measures is to be expected – so that schools adding considerable value would tend to have high examination outcome scores – the relationship shown is too strong for this explanation to be considered sufficient. Value-added analysis is intended to remove the link between a schools’ intake scores and their raw-score outcomes at KS2. It should lead to an estimate of the differential progress made by pupils, assessed between schools. In fact, however, the relationship between value-added and raw scores is of the same size as the original relationship between intake scores and raw-scores that the value-added is intended to overcome. Therefore, however appealing the calculation of value-added figures is, their development is still at the stage where they are not ready to move from being a research tool to an instrument of judgement on schools. Such figures may mislead parents, governors and teachers and, even more importantly, they are being used in England by OFSTED to pre-determine the results of school inspections

Interrelation of structural and electronic properties of InGaN/GaN quantum dots using an eight-band k.p model

We present an eight-band k.p model for the calculation of the electronic structure of wurtzite semiconductor quantum dots (QDs) and its application to indium gallium nitride (InGaN) QDs formed by composition fluctuations in InGaN layers. The eight-band k.p model accounts for strain effects, piezoelectric and pyroelectricity, spin-orbit and crystal field splitting. Exciton binding energies are calculated using the self-consistent Hartree method. Using this model, we studied the electronic properties of InGaN QDs and their dependence on structural properties, i.e., their chemical composition, height, and lateral diameter. We found a dominant influence of the built-in piezoelectric and pyroelectric fields, causing a spatial separation of the bound electron and hole states and a redshift of the exciton transition energies. The single-particle energies as well as the exciton energies depend heavily on the composition and geometry of the QDs