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

Imperfect Entangling Power of Quantum Gates

Achieving perfect control over the parameters defining a quantum gate is, in general, a very challenging task, and at the same time, environmental interactions can introduce disturbances to the initial states as well. Here we address the problem of how the imperfections in unitaries and noise present in the input states affect the entanglement-generating power of a given quantum gate -- we refer to it as imperfect (noisy) entangling power. We observe that, when the parameters of a given unitary are chosen randomly from a Gaussian distribution centered around the desired mean, the quenched average entangling power -- averaged across multiple random samplings -- exhibits intriguing behavior like it may increase or show nonmonotonic behavior with the increase of disorder strength for certain classes of diagonal unitary operators. For arbitrary unitary operators, the quenched average power tends to stabilize, showing almost constant behavior with variation in the parameters instead of oscillating. Our observations also reveal that, in the presence of a local noise model, the input states that maximize the entangling power of a given unitary operator differ considerably from the noiseless scenario. Additionally, we report that the rankings among unitary operators according to their entangling power in the noiseless case change depending on the noise model and noise strength.Comment: 15 pages, 15 figure

Unraveling the Global Teleconnections of Indian Summer Monsoon Clouds: Expedition from CMIP5 to CMIP6

We have analyzed the teleconnection of total cloud fraction (TCF) with global sea surface temperature (SST) in multi-model ensembles (MME) of the fifth and sixth Coupled Model Intercomparison Projects (CMIP5 and CMIP6). CMIP6-MME has a more robust and realistic teleconnection (TCF and global SST) pattern over the extra-tropics (R ~0.43) and North Atlantic (R ~0.39) region, which in turn resulted in improvement of rainfall bias over the Asian summer monsoon (ASM) region. CMIP6-MME can better reproduce the mean TCF and have reduced dry (wet) rainfall bias on land (ocean) over the ASM region. CMIP6-MME has improved the biases of seasonal mean rainfall, TCF, and outgoing longwave radiation (OLR) over the Indian Summer Monsoon (ISM) region by ~40%, ~45%, and ~31%, respectively, than CMIP5-MME and demonstrates better spatial correlation with observation/reanalysis. Results establish the credibility of the CMIP6 models and provide a scientific basis for improving the seasonal prediction of ISM.Comment: 12 pages, 4 main figures, 2 supplementary figure

A circular economy approach for recycling electric motors in the end-of-life vehicles : a literature review

Increasing concerns over climate change have led to global decarbonisation efforts, in the form of new legislation, to phase out the sale of internal combustion engine (ICE) vehicles. As a result, the transition to electrified powertrain vehicles as the mode of transportation has never been greater. Electric motors (EMs), serving as the pivotal component of e-mobility, have gained much attention by policy makers and economic experts concerning the supply chain of raw materials needed for manufacturing. Permanent magnets (PMs), including rare earth elements (REEs), account for 40 to 60 % of the total EM cost. Given the importance of these materials to the e-mobility efforts, there has been a great impetus by leading economies to mitigate supply chain instability and mining operation constraints, by identifying and establishing a sustainable supply source through circular economy strategies. Although extensive studies on REEs recovery, via various techniques, have been undertaken by the research community, there remain underlying concerns over feed source, quality and technical challenges surrounding the retrieval of PM via a functional disassembly approach, all of which are yet to be elucidated. The present study serves to highlight state-of-the-art recycling of EMs from EoL electrified vehicles using a circular economy approach