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

Large Magnetoresistance and Jahn Teller effect in Sr2_2FeCoO6_6

Neutron diffraction measurement on the spin glass double perovskite Sr$_2$FeCoO$_6$ reveals site disorder as well as Co$^{3+}$ intermediate spin state. In addition, multiple valence states of Fe and Co are confirmed through M\"{o}ssbauer and X-ray photoelectron spectroscopy. The structural disorder and multiple valence lead to competing ferromagnetic and antiferromagnetic interactions and subsequently to a spin glass state, which is reflected in the form of an additional $T$-linear contribution at low temperatures in specific heat. A clear evidence of Jahn-Teller distortion at the Co$^{3+}$-O$_6$ complex is observed and incorporating the physics of Jahn-Teller effect, the presence of localized magnetic moment is shown. A large, negative and anomalous magnetoresistance of $\approx$ 63% at 14K in 12T applied field is observed for Sr$_2$FeCoO$_6$. The observed magnetoresistance could be explained by applying a semi-empirical fit consisting of a negative and a positive contribution and show that the negative magnetoresistance is due to spin scattering of carriers by localized magnetic moments in the spin glass phase

Coarse Bifurcation Studies of Bubble Flow Microscopic Simulations

The parametric behavior of regular periodic arrays of rising bubbles is investigated with the aid of 2-dimensional BGK Lattice-Boltzmann (LB) simulators. The Recursive Projection Method is implemented and coupled to the LB simulators, accelerating their convergence towards what we term coarse steady states. Efficient stability/bifurcation analysis is performed by computing the leading eigenvalues/eigenvectors of the coarse time stepper. Our approach constitutes the basis for system-level analysis of processes modeled through microscopic simulations.Comment: 4 pages, 3 figure

Logahedra: A new weakly relational domain

Weakly relational numeric domains express restricted classes of linear inequalities that strike a balance between what can be described and what can be efficiently computed. Popular weakly relational domains such as bounded differences and octagons have found application in model checking and abstract interpretation. This paper introduces logahedra, which are more expressiveness than octagons, but less expressive than arbitrary systems of two variable per inequality constraints. Logahedra allow coefficients of inequalities to be powers of two whilst retaining many of the desirable algorithmic properties of octagons

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