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

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

Boundary Conditions for Fractional Diffusion

This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involve fractional derivatives. The Caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion, since the resulting boundary value problem is not positivity preserving

Prospecting for scarabid specific Bacillus thuringiensis crystal toxin cry8 gene in sugarcane ecosystem of Tamil Nadu, India

In the present study, we report the occurrence of cry8 positive isolates of Bacillus thuringiensis (Bt) in selected white grub, Holotrichia serrata F. (Coleoptera: Scarabaeidae), endemic soils of sugarcane ecosystem and other places in Tamil Nadu. Out of the 66 soil samples collected and screened for white grub specific Bt, 74 isolates of the bacterium, all containing only spherical crystal toxin, were identified. PCR screening of these isolates with cry8 gene universal primer revealed six isolates to be positive. Further, the amplicon of a 370 bp band, amplified with another set of degenerate primer designed based on the conserved sequence of cry8 genes, was sequenced from four isolates. Multiple sequence alignment revealed the gene sequences to be the same for all the isolates. The present report of the availability of cry8 positive Bt isolates opens the avenue for controlling white grubs through transgenic research