Convex Trace Functions on Quantum Channels and the Additivity Conjecture

We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs, if they are applied to the corresponding output state? We prove several results on the structure of the set of those convex functions that are "additive" in this more general sense. In particular, we show that all operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions, which contains the well-known additivity results for this channel as special cases.Comment: 9 pages, 1 figure. Published versio

Quantum correlations and least disturbing local measurements

We examine the evaluation of the minimum information loss due to an unread local measurement in mixed states of bipartite systems, for a general entropic form. Such quantity provides a measure of quantum correlations, reducing for pure states to the generalized entanglement entropy, while in the case of mixed states it vanishes just for classically correlated states with respect to the measured system, as the quantum discord. General stationary conditions are provided, together with their explicit form for general two-qubit states. Closed expressions for the minimum information loss as measured by quadratic and cubic entropies are also derived for general states of two-qubit systems. As application, we analyze the case of states with maximally mixed marginals, where a general evaluation is provided, as well as X states and the mixture of two aligned states.Comment: 10 pages, 3 figure

Accelerating the commercialization of home-grown genetically engineered crops

Transgenic crops offer the state-of-the-art, and yet simple-to-use technologies for sustainable enhancement of agricultural productivity. During the last 20 years, several research groups in India have developed capabilities in genetic engineering of crop plant species and some of them have isolated promising genes and promoters, with potential for commercialization. However, isolated growth of researchers, limited R&D infrastructure and knowledge base available in the seed industry, and the regulatory processes involved in the release of transgenic cultivars pose serious challenges to accelerating the conversion of such leads into field crops. There is an urgent need to evolve efficient managerial approaches for developing and advancing genetically engineered cultivars into Indian agriculture. This article emphasizes the need to identify the most promising transgenics and genes available in the country, evaluate the related intellectual property issues and provide unstinted support to accelerate the process of their commercialization. An approach that would synergize public-public and public-private partnerships needs to be evolved. Initially, it may be driven by public sector through crop- and trait-specific consortia, comprising researchers and the seed industry. A few of such examples should be taken to the stage of clearance by GEAC for unregulated release of indigenously developed transgenic cultivars. These would then serve as role models and catalyse the formation of need-based teams and lasting partnerships, needed to usher Indian agriculture into a globally competitive phase of sustainable productivity

Entropic uncertainty relations and entanglement

We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty relation on one part of the system results in a separability condition on the composite system. We investigate the resulting criteria using the Tsallis entropy for two and three qubits.Comment: 8 pages, 3 figures, v2: small change

Generalized entropic measures of quantum correlations

We propose a general measure of non-classical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure states it reduces to the generalized entanglement entropy, i.e., the generalized entropy of the reduced state. However, in the case of mixed states it can be non-zero in separable states, vanishing just for states diagonal in a general product basis, like the Quantum Discord. Simple quadratic measures of quantum correlations arise as a particular case of the present formalism. The minimum information loss due to a joint local measurement is also discussed. The evaluation of these measures in a few simple relevant cases is as well provided, together with comparison with the corresponding entanglement monotones.Comment: 9 pages, 2 figure

Generating qudits with d=3,4 encoded on two-photon states

We present an experimental method to engineer arbitrary pure states of qudits with d=3,4 using linear optics and a single nonlinear crystal.Comment: 4 pages, 1 eps figure. Minor changes. The title has been changed for publication on Physical Review

Purification and characterization of two major lectins from Vigna mungo (blackgram)

Blackgram (Vigna mungo L. Hepper) seeds contain two galactose-specific lectins, BGL-I and BGL-II. BGL-I was partially purified into two monomeric lectins which were designated as BGL-I-1 (94 kDa) and BGL-I-2 (89 kDa). BGL-II is a monomeric lectin of 83 kDA. The purified lectins were associated with galactosidase activities. BGL-I-1 and BGL-II were copurified with α-galactosidase activity while BGL-I-2 was largely associated with β-galactosidase activity. These lectins agglutinate trypsin treated rabbit erythrocytes, but not the human erythrocytes of A, B or O groups. They were stable between pH 3.5 and 7.5 for their agglutination. The lectins did not show any metalion requirement. They were inactivated at 50°C. The lectin activity was inhibited by D-galactose (0.1 mM). The Scatchard plots of galactose binding to these lectins are nonlinear and biphasic curves indicative of multiple binding sites. The data show that the monomeric lectins have both lectin and galactosidase activities suggestive of a bifunctional protein

Generalized Induced Norms

Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n. We will investigate this problem and its various aspects and will discuss under which conditions ||.||_1=||.||_2.Comment: 8 page

A Detailed Analysis of a Cygnus Loop Shock-Cloud Interaction

The XA region of the Cygnus Loop is a complex zone of radiative and nonradiative shocks interacting with interstellar clouds. We combine five far ultraviolet spectral observations from the Hopkins Ultraviolet Telescope (HUT), a grid of 24 IUE spectra and a high-resolution longslit Halpha spectrum to study the spatial emission line variations across the region. These spectral data are placed in context using ground-based, optical emission line images of the region and a far-UV image obtained by the Ultraviolet Imaging Telescope (UIT). The presence of high-ionization ions (OVI, NV, CIV) indicates a shock velocity near 170 km/s while other diagnostics indicate v_shock=140 km/s. It is likely that a large range of shock velocities may exist at a spatial scale smaller than we are able to resolve. By comparing CIV 1550, CIII 977 and CIII] 1909, we explore resonance scattering across the region. We find that a significant column depth is present at all positions, including those not near bright optical/UV filaments. Analysis of the OVI doublet ratio suggests an average optical depth of about unity in that ion while flux measurements of [SiVIII] 1443 suggest a hot component in the region at just below 10^6K. Given the brightness of the OVI emission and the age of the interaction, we rule out the mixing layer interpretation of the UV emission. Furthermore, we formulate a picture of the XA region as the encounter of the blast wave with a finger of dense gas protruding inward from the pre-SN cavity.Comment: 21 pages, 9 figures, accepted by the Astronomical Journal, July 2001 Full resolution figures available at http://fuse.pha.jhu.edu/~danforth/xa