Characterizing the geometrical edges of nonlocal two-qubit gates

Nonlocal two-qubit gates are geometrically represented by tetrahedron known as Weyl chamber within which perfect entanglers form a polyhedron. We identify that all edges of the Weyl chamber and polyhedron are formed by single parametric gates. Nonlocal attributes of these edges are characterized using entangling power and local invariants. In particular, SWAP (power)alpha family of gates constitutes one edge of the Weyl chamber with SWAP-1/2 being the only perfect entangler. Finally, optimal constructions of controlled-NOT using SWAP-1/2 gate and gates belong to three edges of the polyhedron are presented.Comment: 11 pages, 4 figures, Phys. Rev. A 79, 052339 (2009

Improvements in aircraft extraction programs

Flight data from an F-8 Corsair and a Cessna 172 was analyzed to demonstrate specific improvements in the LRC parameter extraction computer program. The Cramer-Rao bounds were shown to provide a satisfactory relative measure of goodness of parameter estimates. It was not used as an absolute measure due to an inherent uncertainty within a multiplicative factor, traced in turn to the uncertainty in the noise bandwidth in the statistical theory of parameter estimation. The measure was also derived on an entirely nonstatistical basis, yielding thereby also an interpretation of the significance of off-diagonal terms in the dispersion matrix. The distinction between coefficients as linear and non-linear was shown to be important in its implication to a recommended order of parameter iteration. Techniques of improving convergence generally, were developed, and tested out on flight data. In particular, an easily implemented modification incorporating a gradient search was shown to improve initial estimates and thus remove a common cause for lack of convergence

Magnetic properties of geometrically frustrated SrGd2O4

A study of the magnetic properties of the frustrated rare earth oxide SrGd2O4 has been completed using bulk property measurements of magnetization, susceptibility and specific heat on single crystal samples. Two zero-field phase transitions have been identified at 2.73 and 0.48 K. For the field, H, applied along the a and b axes, a single boundary is identified that delineates the transition from a low field, low temperature magnetically ordered regime to a high field, high temperature paramagnetic phase. Several field-induced transitions, however, have been observed with H || c. The measurements have been used to map out the magnetic phase diagram of SrGd2O4, suggesting that it is a complex system with several competing magnetic interactions. The low-temperature magnetic behavior of SrGd2O4 is very different compared to the other SrLn2O4 (Ln = Lanthanide) compounds, even though all of the SrLn2O4 compounds are isostructural, with the magnetic ions forming a low-dimensional lattice of zigzag chains that run along the c axis. The differences are likely to be due to the fact that in the ground state Gd3+ has zero orbital angular momentum and therefore the spin-orbit interactions, which are crucial for other SrLn2O4 compounds, can largely be neglected. Instead, given the relatively short Gd3+-Gd3+ distances in SrGd2O4, dipolar interactions must be taken into account for this antiferromagnet alongside the Heisenberg exchange terms.Comment: 10 pages, 9 figure

Entangling characterization of (SWAP)1/m and Controlled unitary gates

We study the entangling power and perfect entangler nature of (SWAP)1/m, for m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only perfect entangler in the family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.Comment: 12 pages, 1 figure, One more paragraph added in Introductio

Studies of the superconducting properties of Sn1-xInxTe (x=0.38 to 0.45) using muon-spin spectroscopy

The superconducting properties of Sn1-xInxTe (x = 0.38 to 0.45) have been studied using magnetization and muon-spin rotation or relaxation (muSR) measurements. These measurements show that the superconducting critical temperature Tc of Sn1-xInxTe increases with increasing x, reaching a maximum at around 4.8 K for x = 0.45. Zero-field muSR results indicate that time-reversal symmetry is preserved in this material. Transverse-field muon-spin rotation has been used to study the temperature dependence of the magnetic penetration depth lambda(T) in the mixed state. For all the compositions studied, lambda(T) can be well described using a single-gap s-wave BCS model. The magnetic penetration depth at zero temperature lambda(0) ranges from 500 to 580 nm. Both the superconducting gap Delta(0) at 0 K and the gap ratio Delta(0)/kBTc indicate that Sn1-xInxTe (x = 0.38 to 0.45) should be considered as a superconductor with intermediate to strong coupling.Comment: 7 pages, 6 figures, 3 table

Superconducting and normal-state properties of the noncentrosymmetric superconductor Re6Zr

We systematically investigate the normal and superconducting properties of non-centrosymmetric Re$_{6}$Zr using magnetization, heat capacity, and electrical resistivity measurements. Resistivity measurements indicate Re$_{6}$Zr has poor metallic behavior and is dominated by disorder. Re$_6$Zr undergoes a superconducting transition at $T_{\mathrm{c}} = \left(6.75\pm0.05\right)$ K. Magnetization measurements give a lower critical field, $\mu_{0}H_{\mathrm{c1}} = \left(10.3 \pm 0.1\right)$ mT. The Werthamer-Helfand-Hohenberg model is used to approximate the upper critical field $\mu_{0}H_{\mathrm{c2}} = \left(11.2 \pm 0.2\right)$ T which is close to the Pauli limiting field of 12.35 T and which could indicate singlet-triplet mixing. However, low-temperature specific-heat data suggest that Re$_{6}$Zr is an isotropic, fully gapped s-wave superconductor with enhanced electron-phonon coupling. Unusual flux pinning resulting in a peak effect is observed in the magnetization data, indicating an unconventional vortex state.Comment: 11 pages, 7 figures, 2 table

Magnetic phase diagram of the antiferromagnetic pyrochlore Gd2Ti2O7

Gd2Ti2O7 is a highly frustrated antiferromagnet on a pyrochlore lattice, where apart from the Heisenberg exchange the spins also interact via dipole-dipole forces. We report on low-temperature specific heat measurements performed on single crystals of Gd2Ti2O7 for three different directions of an applied magnetic field. The measurements reveal the strongly anisotropic behaviour of Gd2Ti2O7 in a magnetic field despite the apparent absence of a significant single-ion anisotropy for Gd3+. The H-T phase diagrams are constructed for H//111], H//[110] and H//[112]. The results indicate that further theoretical work beyond a simple mean-field model is required.Comment: 4 figure

On The Center Sets and Center Numbers of Some Graph Classes

For a set $S$ of vertices and the vertex $v$ in a connected graph $G$, $\displaystyle\max_{x \in S}d(x,v)$ is called the $S$-eccentricity of $v$ in $G$. The set of vertices with minimum $S$-eccentricity is called the $S$-center of $G$. Any set $A$ of vertices of $G$ such that $A$ is an $S$-center for some set $S$ of vertices of $G$ is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, $K_{m,n}$, $K_n-e$, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes