Hierarchies among Genuine Multipartite Entangling Capabilities of Quantum Gates

We categorize quantum gates according to their capability to generate genuine multipartite entanglement based on the hierarchy of multipartite separable states. In particular, when a fixed unitary operator acts on the set of k-separable states, the maximal (average) genuine multipartite entanglement (GME) content produced via that particular unitary operator is determined after maximizing over the set of k-separable input states. We identify unitary operators that are beneficial for generating high GME when the input states are entangled in some bipartition, although the picture can also be reversed in which entanglement in inputs does not help. We characterize maximum entangling power of a variety of unitary operators including special classes of quantum gates, diagonal, permutation and Haar uniformly generated unitary operators by computing generalized geometric measure (GGM) as GME quantifier. We determine the unitary operators and their corresponding inputs which can create the resulting states having maximum GGM.Comment: v1: 8 pages, 8 figures; v2: 11 pages, 6 figures, new sections including new results adde

Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms

A Rota-Baxter Lie algebra $\mathfrak{g}_T$ is a Lie algebra $\mathfrak{g}$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie algebra $\mathfrak{g}_T$ by another Rota-Baxter Lie algebra $\mathfrak{h}_S.$ We define the non-abelian cohomology $H^2_{nab} (\mathfrak{g}_T, \mathfrak{h}_S)$ which classifies {equivalence classes of} such extensions. Given a non-abelian extension $$0 \rightarrow \mathfrak{h}_S \xrightarrow{i} \mathfrak{e}_U \xrightarrow{p} \mathfrak{g}_T \rightarrow 0$$ of Rota-Baxter Lie algebras, we also show that the obstruction for a pair of Rota-Baxter automorphisms in $\mathrm{Aut}(\mathfrak{h}_S ) \times \mathrm{Aut}(\mathfrak{g}_T)$ to be induced by an automorphism in $\mathrm{Aut}(\mathfrak{e}_U)$ lies in the cohomology group $H^2_{{nab}} (\mathfrak{g}_T, \mathfrak{h}_S)$. As a byproduct, we obtain the Wells short-exact sequence in the context of Rota-Baxter Lie algebras.Comment: Any comments/suggestions are welcom

Impact of management protocols of intrauterine fetal death on perceived stress: A comparative study

Background: Pregnancy loss is a distressing problem and retention of dead fetus in utero has its own ill effects on physical, psychological, and social aspects, and hence, it is better to recommend medical induction, provided this can be safely undertaken. Aims: The aim of this study is to compare the efficacy, tolerability, induction-delivery interval, and perceived stress scores between induction methods in late intrauterine fetal death (IUFD) with misoprostol alone and mifepristone with misoprostol combination in a rural population of Eastern India. Materials and Methods: This pilot study was conducted on 125 patients after taking institutional ethical clearance and informed consent of the patients in a time span of 1 year. Group 2 patients received 200 mg of mifepristone per orally and observed for 48 h, followed by 50 μg misoprostol administered in the posterior vaginal fornix, and repeated 6th hourly up to a maximum of four doses. Group 1 received 50 μg misoprostol per vaginally 6 hourly for four doses. Induction-delivery interval was calculated. Perceived stress level was calculated on admission and before discharge. Results: Significantly lower induction-delivery interval was observed in Group 2 as compared to Group 1 with P < 0.001. There was no significant difference of Cohen's perceived stress scores on admission, but the difference was significantly lower in Group 2 on discharge with the value of P = 0.03. Group 1 had significantly lower hospital stay in days as compared to Group 2 of patients with P < 0.001. Conclusions: Patients with IUFD administered misoprostol per vaginally only may require shorter hospital stay as compared to patients administered with oral mifepristone followed by misoprostol vaginally but the delivery induction time increases significantly and may increase perceived stress levels which may have short- and long-term negative psychological impact