Optimal Protocols for Nonlocality Distillation

Forster, Winkler, and Wolf recently showed that weak nonlocality can be amplified by giving the first protocol that distills a class of nonlocal boxes (NLBs) [Phys. Rev. Lett. 102, 120401 (2009)]. We first show that their protocol is optimal among all non-adaptive protocols. We next consider adaptive protocols. We show that the depth 2 protocol of Allcock et al. [Phys. Rev. A 80, 062107, (2009)] performs better than previously known adaptive depth 2 protocols for all symmetric NLBs. We present a new depth 3 protocol that extends the known region of distillable NLBs. We give examples of NLBs for which each of Forster et al.'s, Allcock et al.'s, and our protocol performs best. The new understanding we develop is that there is no single optimal protocol for NLB distillation. The choice of which protocol to use depends on the noise parameters for the NLB.Comment: RevTeX4, 6 pages with 4 figure

Quantum Nonlocal Boxes Exhibit Stronger Distillability

The hypothetical nonlocal box (\textsf{NLB}) proposed by Popescu and Rohrlich allows two spatially separated parties, Alice and Bob, to exhibit stronger than quantum correlations. If the generated correlations are weak, they can sometimes be distilled into a stronger correlation by repeated applications of the \textsf{NLB}. Motivated by the limited distillability of \textsf{NLB}s, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (\textsf{qNLB}s). We propose a new protocol for distillation and show that it asymptotically distills a class of correlated quantum nonlocal boxes to the value $1/2 (3\sqrt{3}+1) \approx 3.098076$, whereas in contrast, the optimal non-adaptive parity protocol for classical nonlocal boxes asymptotically distills only to the value 3.0. We show that our protocol is an optimal non-adaptive protocol for 1, 2 and 3 \textsf{qNLB} copies by constructing a matching dual solution for the associated primal semidefinite program (SDP). We conclude that \textsf{qNLB}s are a stronger resource for nonlocality than \textsf{NLB}s. The main premise that develops from this conclusion is that the \textsf{NLB} model is not the strongest resource to investigate the fundamental principles that limit quantum nonlocality. As such, our work provides strong motivation to reconsider the status quo of the principles that are known to limit nonlocal correlations under the framework of \textsf{qNLB}s rather than \textsf{NLB}s.Comment: 25 pages, 7 figure

Advances in Halloysite Nanotubes (HNTs)-Based Mixed-Matrix Membranes for CO2 Capture

Membrane technology promises a highly economical and efficient solution for CO2 separation. Many polymeric membranes have been reported in the past for the separation of gases specially to remove CO2 from natural gas and low-pressure flue-gas streams. The performance of membranes can be tailored by dispersing nanofillers in a polymeric matrix to produce mixed-matrix membranes (MMMs). This not only adds mechanical strength to membranes but also reduces compaction of the polymeric layer at high pressure and maintains high performance. Halloysite nanotubes (HNTs) gained attention in gas separation technology and due to their tubular structure have been used in a variety of applications in biomedical, coating, composite, and electronic industries. However, very little but conclusive literature and reviews are available to indicate that functionalized and non-functionalized HNTs can improve the performance of MMMs for efficient CO2 capture. The current status and gaps for potential applications of HNTs-based membranes for gas separation are identified and reviewed

Nonlocality and the no-signalling polytope

Bibliography: p. 86-9

Limits and consequesnces of nonlocality distillation

Bibliography: p. 93-106Only in the last few decades have we realized how to view quantum nonlocal correlations as possible information theoretic resources rather than as apparent paradoxes. Unfortunately, the past perspective in terms of paradoxes still persists in our considerations of nonlocal boxes (NLBs) that offer stronger than quantum nonlocal correlations. We argue that a more pragmatic approach is to consider the physical framework under which such correlations may be realized. Our consideration immediately yields fruit by allowing us to identify limitations of the NLB model and develop the generalized notion of a quantum nonlocal box (qNLB). We analyze the NLB and qNLB models within the framework of nonlocality distillation protocols. The ability to concentrate the correlations of many identical noisy copies of a nonlocal correlation source is known as nonlocality distillation. The idea is still in its early stages of development and and we pursue it in this thesis. We develop multiple new nonlocality distillation protocols and prove the optimality of non-adaptive distillation protocols for both NLBs and qNLBs. We show that qNLBs offer stronger non-adaptive distillation protocols than NLBs. At the same time, the understanding we develop is that there is no single optimal adaptive protocol for N LB distillation. The choice of which protocol to use depends on the noise parameters for the NLB. Through our investigation of nonlocality distillation protocols we conclude that the qNLB model is a stronger resource for nonlocality than NLBs. The main premise that develops from this conclusion is that the N LB model is not the strongest resource to investigate the fundamental principles that limit quantum nonlocality. As such, our work provides strong motivation to reconsider the status quo of the principles that limit nonlocal correlations under the framework of qNLBs rather than NLBs. As a first step towards the re-examination of such principles, we provide numerical evidence that the distillability of nonlocal correlations depends on properties that are local. We claim that the differing strength of distillation protocols for NLBs and qNLBs can be interpreted as a separation between classical and quantum predictions at the macroscopic level. This implies that there exist quantum correlations that can be observed in principle, at the macroscopic level or that the principle of macroscopic locality identifies exactly the set of quantum correlations

Iterative Solutions of Hirota Satsuma Coupled KDV and Modified Coupled KDV Systems

In this article the approximate solutions of nonlinear Hirota Satsuma coupled Korteweg De- Vries (KDV) and modified coupled KDV equations have been obtained by using reliable algorithm of New Iterative Method (NIM). The results obtained give higher accuracy than that of homotopy analysis method (HAM). The obtained solutions show that NIM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution

New Iterative Method for the Solution of Fractional Damped Burger and Fractional Sharma-Tasso-Olver Equations

The new iterative method has been used to obtain the approximate solutions of time fractional damped Burger and time fractional Sharma-Tasso-Olver equations. Results obtained by the proposed method for different fractional-order derivatives are compared with those obtained by the fractional reduced differential transform method (FRDTM). The 2nd-order approximate solutions by the new iterative method are in good agreement with the exact solution as compared to the 5th-order solution by the FRDTM

Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations

In this paper, the Optimal Homotopy Asymptotic Method is extended to derive the approximate solutions of fractional order two-dimensional partial differential equations. The fractional order Zakharov–Kuznetsov equation is solved as a test example, while the time fractional derivatives are described in the Caputo sense. The solutions of the problem are computed in the form of rapidly convergent series with easily calculable components using Mathematica. Reliability of the proposed method is given by comparison with other methods in the literature. The obtained results showed that the method is powerful and efficient for determination of solution of higher-dimensional fractional order partial differential equations