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

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

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

Affordable voltammetric sensor based on anodized disposable pencil graphite electrodes for sensitive determination of dopamine and uric acid in presence of high concentration of ascorbic acid

A simple, disposable and low - cost voltammetric sensor based on the anodized pencil graphite electrode (APGE) for the simultaneous determination of dopamine (DA) and uric acid (UA) is demonstrated. The physico-chemical properties of the pencil graphite electrode (PGE) before and after anodization were analyzed using FT-IR, FT-Raman, SEM and EIS characterization techniques. In comparison to PGE, APGE exhibited excellent electrochemical activity towards the simultaneous detection of DA and UA with peak-to-peak separation of about 0.18 V even in the presence of high concentration (2 mM) of ascorbic acid (AA). The discrimination of APGE towards AA was rationalized through the absence of favorable surface interactions between oxygen rich functional groups on the surface of APGE and AA. Using DPV without any pre-concentration step and under optimized conditions, APGE displayed a linear range of 1 – 80 μM with an estimated limit of detection (LOD, 3σ/m) of 0.008 μM and 0.014 μM for DA and UA, respectively. Moreover, a higher sensitivity in comparison to other previously reported pretreated pencil graphite electrodes was observed for DA (34.32 μA/μM) and UA (12.33 μA/μM). The practical applicability of APGE was demonstrated through the estimation of DA in human blood serum and UA in urine samples