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

Catalytic Conversion Probabilities for Bipartite Pure States

For two given bipartite-entangled pure states, an expression is obtained for the least upper bound of conversion probabilities using catalysis. The attainability of the upper bound can also be decided if that bound is less than one.Comment: 4 pages; comments appreciated; the article is a modified version of this preprint combined with arXiv:0707.044

No Tension Approach to Define Failure Phenomena for Rockfill Dam Subjected to Earthquake Loading

It has been observed that actual behavior of Rockfill dams during earthquake is much different than that obtained by elastic analysis. No tension approach has thus been developed to overcome the shortfalls of elastic analysis. Using no tension approach redistribution of stresses are obtained which help in defining the failure pattern of the dam\u27 subjected to a given seismic acceleration or in other words the failure acceleration is obtained for a given dam subjected to earthquake forces. Various dam models having different upstream and downstream slopes are analyzed using finite element technique. The input earthquake motion has been considered as an equivalent static force. Anisotropy of the rockfill material has been considered. The failure acceleration level for various dam models having different upstream and downstream slopes are thus evaluated. The results are compared with those obtained experimentally and show a good agreement

Majorization criterion for distillability of a bipartite quantum state

Bipartite quantum states are classified into three categories: separable states, bound entangled states, and free entangled states. It is of great importance to characterize these families of states for the development of quantum information science. In this paper, I show that the separable states and the bound entangled states have a common spectral property. More precisely, I prove that for undistillable -- separable and bound entangled -- states, the eigenvalue vector of the global system is majorized by that of the local system. This result constitutes a new sufficient condition for distillability of bipartite quantum states. This is achieved by proving that if a bipartite quantum state satisfies the reduction criterion for distillability, then it satisfies the majorization criterion for separability.Comment: 4 pages, no figures, REVTEX. A new lemma (Lemma 2) added. To appear in Physical Review Letter

Extremal extensions of entanglement witnesses: Unearthing new bound entangled states

In this paper, we discuss extremal extensions of entanglement witnesses based on Choi's map. The constructions are based on a generalization of the Choi map due to Osaka, from which we construct entanglement witnesses. These extremal extensions are powerful in terms of their capacity to detect entanglement of positive under partial transpose (PPT) entangled states and lead to unearthing of entanglement of new PPT states. We also use the Cholesky-like decomposition to construct entangled states which are revealed by these extremal entanglement witnesses.Comment: 8 pages 6 figures revtex4-

Hypolipidemic, Hypoglycemic and Anti-oxidant Activities of Flower Extracts of Allamanda Violacea A. DC (Apocynaceae)

Purpose: To investigate the anti-dyslipidemic, anti-oxidant and anti-diabetic activities of the aqueous extract and solvent fractions of A. violacea flowers.Methods: The aqueous extract was fractionated into petroleum ether, ether, chloroform, chloroformmethanol (4:1) and chloroform-methanol (3:2) fractions. Lipid lowering activity was evaluated in two models, viz, triton WR-1339 - induced hyperlipimea in rats as well as fructose-rich high fat diet. To assess anti-oxidant activity, in-vitro model of non-enzymic superoxide hydroxyl radicals and microsomal lipid peroxidation by non-enzymic inducer was adopted. Hypoglycemic activity was evaluated by sucrose-loaded rat model.Results: Amongst the fractions, ether and chloroform fractions caused marked decrease in the levels of total cholesterol (Tc), triglycerides (Tg), plasma lipids (Pl), and protein by 24, 23, 23 and 22 %, and 24, 22, 23 and 19 %, respectively. In rats fed with high fat diet (HFD), ether and chloroform fractions lowered Tc, Tg and, Pl by 26, 25 and 26 %, and 18, 19 and 20 %, respectively. Significant decrease in superoxide anions, hydroxyl radicals and microsomal lipid peroxidation by ether and chloroform fractions was also observed. Chloroform, chloroform-methanol (4:1) and chloroform-methanol (3:2) fractions showed antihyperglycaemic activity to the extent of 25.2, 21.6 and 23.2 %, respectively.Conclusion: The flowers of this plant, especially the ether and chloroform extracts, may be suitable as an anti-oxidant supplement for lipid management.Keywords: Allamanda violacea flowers, Anti-hyperlipidemic,  Anti-hyperglycemic, Anti-oxidant

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

Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints

For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+\beta,\,\max\{2,\,1+\ln\frac{1}{\beta}\})$ is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-$(1.369,\,2)$ approximation algorithm by setting $1+\ln\frac{1}{\beta}=2$ and a factor-$(1.567,\,1.567)$ algorithm by setting $1+\beta=1+\ln\frac{1}{\beta}$. Besides, by setting $\beta=0$, an approximation algorithm with ratio $(1,\, O(\ln n))$, i.e. an algorithm with only a single factor ratio $O(\ln n)$ on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the $k$BCP problem that strictly obeys the delay constraint.Comment: 12 page

Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs

We address the question of the multiplicativity of the maximal p-norm output purities of bosonic Gaussian channels under Gaussian inputs. We focus on general Gaussian channels resulting from the reduction of unitary dynamics in larger Hilbert spaces. It is shown that the maximal output purity of tensor products of single-mode channels under Gaussian inputs is multiplicative for any p>1 for products of arbitrary identical channels as well as for a large class of products of different channels. In the case of p=2 multiplicativity is shown to be true for arbitrary products of generic channels acting on any number of modes.Comment: 9 page