A scheme of quantum state discrimination over specified states via weak-value measurement

The commonly adopted projective measurements are invalid in the specified task of quantum state discrimination when the discriminated states are superposition of planar-position basis states whose complex-number probability amplitudes have the same magnitude but different phases. Therefore we propose a corresponding scheme via weak-value measurement and examine the feasibility of this scheme. Furthermore, the role of the weak-value measurement in quantum state discrimination is analyzed and compared with one in quantum state tomography in this Letter.     

Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 9

Let $k$ be a positive integer. An adjacent vertex distinguishing (for short, AVD) total-$k$-coloring of a graph $G$ is a proper total-$k$-coloring of $G$ such that any two adjacent vertices have different color sets, where the color set of a vertex $v$ contains the color of $v$ and the colors of its incident edges. It was conjectured that any graph with maximum degree $\Delta$ has an AVD total-($\Delta +3$)-coloring. The conjecture was confirmed for any graph with maximum degree at most 4 and any planar graph with maximum degree at least 10. In this paper, we verify the conjecture for all planar graphs with maximum degree at least 9. Moreover, we prove that any planar graph with maximum degree at least 10 has an AVD total-($\Delta +2$)-coloring and the bound $\Delta +2$ is sharp.     

Optical waveguide with homogeneous refractive index profile in LiNbO3 by double-low-energy Oxygen ion implantation

We report on the formation of the planar waveguide by 550 keV O ion followed by 250 keV O ion implantation in lithium niobate (LiNbO₃), at fluences of 6 × 10¹⁴ ions/cm² and 3 × 10¹⁴ ions/cm², respectively. The Rutherford backscattering/channeling spectra have shown the atomic displacements in the damage region before and after annealing. A broad and nearly homogeneous damage layer has been formed by double-energy ion implantation after annealing. Both the dark mode spectra and the data of refractive index profile verified that the extraordinary refractive index was enhanced in the ion implanted region of LiNbO₃. A homogeneous near-field intensity profile was obtained by double-low-energy ion implantation. There is a reasonable agreement between the simulated modal intensity profile and the experimental data. The estimated propagation loss is about 0.5 dB/cm.     

A 1 × 4 polarization and wavelength independent optical power splitter based on a novel wide-angle low-loss Y-junction

A 1 × 4 polarization and wavelength independent optical power splitter is reported. This device is based on a novel wide-angle low-loss Y-junction structure which can give a theoretical TE junction excess loss of 0.26 dB at a branching angle of 16°. To the best of our knowledge, it is so far the lowest reported loss at such a large angle. The detailed design of the device and its fabrication are described. Our experimental results show the measured TE excess loss to be 1.2 dB and TM excess loss 1.8 dB for the whole splitter over the wavelength between 1.47 μm and 1.57 μm.     

Laminar boundary layer separation at a fin-body junction in a hypersonic flow

Planar laser-induced fluorescence (PLIF) imaging was performed to visualize the fin bow shock, separation shock, viscous shear layer and recirculation region of the flowfield at the junction of a blunt fin and a flat plate. Making use of the temperature dependence of the PLIF technique, images were made sensitive to temperature to provide qualitative information on the flowfield. The PLIF technique was also used as the basis for a flow-tagging technique, making it possible to measure a velocity component and to demonstrate the reverse flow of the separated region. Flow visualisation of the plane of symmetry allowed determination of the point of boundary layer separation, the angle of the separation shock and the bow shock standoff distance. These parameters were compared with predictions made by computational fluid dynamic simulations of the flowfield. Good agreement between theory and experiment was achieved. Comparisons between theoretical and experimental velocity measurements showed good agreement. Received 17 October 2000 / Accepted 13 November 2000     

Homomorphisms of planar (m,n)-colored-mixed graphs to planar targets

An $(m,n)$-colored-mixed graph $G=(V,A_1,A_2,\cdots ,A_m,E_1,E_2,\cdots ,E_n)$ is a graph having m colors of arcs and n colors of edges. We do not allow two arcs or edges to have the same endpoints. A homomorphism from an $(m,n)$-colored-mixed graph G to another $(m,n)$-colored-mixed graph H is a morphism $\phi :V(G)\to V(H)$ such that each edge (resp. arc) of G is mapped to an edge (resp. arc) of H of the same color (and orientation). An $(m,n)$-colored-mixed graph T is said to be $P_g^{(m,n)}$-universal if every graph in $P_g^{(m,n)}$ (the planar $(m,n)$-colored-mixed graphs with girth at least g) admits a homomorphism to T.We show that planar $P_g^{(m,n)}$-universal graphs do not exist for $2m+n\ge 3$ (and any value of g) and find a minimal (in the number vertices) planar $P_g^{(m,n)}$-universal graphs in the other cases.