Optimal Decompositions of Barely Separable States

Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble --- the ensemble realizing the entanglement of formation --- is greater than the rank of the mixed state. We find examples for which the number of states in this optimal ensemble can be larger than the rank by an arbitrarily large factor. In one case the proof relies on the fact that the partial transpose of the mixed state has zero eigenvalues; in the other case the result arises from the properties of product bases that are completable only by embedding in a larger Hilbert space.Comment: 14 Pages (RevTeX), 1 figure (eps). Submitted to the special issue of the J. Mod. Opt. V2: Change in terminology from "ensemble length" to "ensemble cardinality

Mobility Robustness in 5G Networks

5G is the 5th Generation of Mobile telecommunication system. 5G networks will cater to the needs of very diverse user equipment, from millions of stationary sensors per square kilometer to bullet trains running at over 500 km/h. Presence of users with such varied mobility requirements entails us to build a robust mobility architecture for 5G. Two of the important requirements for 5G networks are a lower latency and a higher reliability than in existing generations of mobile networks. To accomplish the above mentioned use cases and requirements of 5G networks, the mobility solutions and their robustness become a very critical part of 5G. In this thesis we have studied the existing LTE networks, and keeping them as a baseline, tried to find solutions for mobility robustness in 5G networks. The thesis discusses Mobility State Estimation (MSE) enhancements for dual and multiconnectivity. Analysis of mobility problems in using only one instance of mobility state for a multi-link, multi-layer connected UE are quantitatively analysed and a solution, which uses a MSE instance for each link in multi-link connectivity, is proposed. Other mobility robustness topic that the thesis focuses upon is improvements in handover failure recovery mechanism, which can also be used for radio link failure in general. The thesis proposes a solution for re-establishment of RRC connection in 5G by using the RRC Connection Suspend and RRC Connection Resume procedure of Narrow Band Inter of Things (NB-IoT)

IN SILICO MODELING OF MONOMERIC DEXAMETHASONE-INDUCED RAS-RELATED PROTEIN 1 AND RAS HOMOLOG ENRICHED IN STRIATUM: ROLE OF N TERMINUS AND STRUCTURE‑FUNCTION RELATIONSHIP

Objective: Dexamethasone-induced Ras-related protein 1 (Dexras1) and Ras homolog enriched in striatum (RHES) are the two monomeric small G proteins that belong to Ras superfamily. These two proteins show 62% similarity. Both of these proteins are involved in signaling and modulation of several pathophysiological processes. They have unique GTP binding domain and a unique C and N terminus. C terminus is known to interact with several proteins; however, the role of its unique N terminus is still not known. The three-dimensional (3D) structure of these proteins is also not available in any of the databases yet. This present study approaches bioinformatics tools and servers to predict the 3D structure of these two proteins in silico.Methods: In this study, two bioinformatics servers were used, namely Swiss modeling server and Iterative Threading ASSEmbly Refinement (I-TASSER) server.Results: Both servers developed many alignment templates of Dexras1 and RHES. These alignments were used to develop 3D structure using Pymol. These models have different regions of proteins such as N terminus, GTP-binding domains, effector loop, C terminus, and the unique CAAX site. The models deduce that the N-terminals of both Dexras1 and RHES are unique regions that might possible be dangling out of the protein while it gets inserted into the membrane. We hypothesize that this unique N-terminal might have a distinct role in the modulation of N-type calcium channels.Conclusion: All the models generated show predicted 3D structure of Dexras1 and RHES protein. This study of structural prediction will be helpful in knowing the interaction of Dexras1 and RHES and a step forward to target these two proteins as a novel therapeutic drug

Exact and Asymptotic Measures of Multipartite Pure State Entanglement

In an effort to simplify the classification of pure entangled states of multi (m) -partite quantum systems, we study exactly and asymptotically (in n) reversible transformations among n'th tensor powers of such states (ie n copies of the state shared among the same m parties) under local quantum operations and classical communication (LOCC). With regard to exact transformations, we show that two states whose 1-party entropies agree are either locally-unitarily (LU) equivalent or else LOCC-incomparable. In particular we show that two tripartite Greenberger-Horne-Zeilinger (GHZ) states are LOCC-incomparable to three bipartite Einstein-Podolsky-Rosen (EPR) states symmetrically shared among the three parties. Asymptotic transformations result in a simpler classification than exact transformations. We show that m-partite pure states having an m-way Schmidt decomposition are simply parameterizable, with the partial entropy across any nontrivial partition representing the number of standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the state in question. For general m-partite states, partial entropies across different partitions need not be equal, and since partial entropies are conserved by asymptotically reversible LOCC operations, a multicomponent entanglement measure is needed, with each scalar component representing a different kind of entanglement, not asymptotically interconvertible to the other kinds. In particular the m=4 Cat state is not isentropic to, and therefore not asymptotically interconvertible to, any combination of bipartite and tripartite states shared among the four parties. Thus, although the m=4 cat state can be prepared from bipartite EPR states, the preparation process is necessarily irreversible, and remains so even asymptotically.Comment: 13 pages including 3 PostScript figures. v3 has updated references and discussion, to appear Phys. Rev.

End-to-end Dense Video Captioning as Sequence Generation

Dense video captioning aims to identify the events of interest in an input video, and generate descriptive captions for each event. Previous approaches usually follow a two-stage generative process, which first proposes a segment for each event, then renders a caption for each identified segment. Recent advances in large-scale sequence generation pretraining have seen great success in unifying task formulation for a great variety of tasks, but so far, more complex tasks such as dense video captioning are not able to fully utilize this powerful paradigm. In this work, we show how to model the two subtasks of dense video captioning jointly as one sequence generation task, and simultaneously predict the events and the corresponding descriptions. Experiments on YouCook2 and ViTT show encouraging results and indicate the feasibility of training complex tasks such as end-to-end dense video captioning integrated into large-scale pre-trained models