Large violation of Bell inequalities with low entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order $\frac{\sqrt{n}}{\log n}$ with $n$ inputs, $n$ outputs and $n$-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the Entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.Comment: Reference [16] added. Some typos correcte

On the relationship between continuous- and discrete-time quantum walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian oracles; v3: published version, with improved analysis of phase estimatio

Superselectors: Efficient Constructions and Applications

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel conflict resolution and data security. We prove close upper and lower bounds on the size of superselectors and we provide efficient algorithms for their constructions. Albeit our bounds are very general, when they are instantiated on the combinatorial structures that are particular cases of superselectors (e.g., (p,k,n)-selectors, (d,\ell)-list-disjunct matrices, MUT_k(r)-families, FUT(k, a)-families, etc.) they match the best known bounds in terms of size of the structures (the relevant parameter in the applications). For appropriate values of parameters, our results also provide the first efficient deterministic algorithms for the construction of such structures

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape

Eigenvectors of the discrete Laplacian on regular graphs - a statistical approach

In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical observations, suggesting that the eigenvectors follow a Gaussian distribution. Following this assumption, we reconstruct some properties of the nodal structure which were observed in numerical simulations, but were not explained so far. We also show that some statistical properties of the nodal pattern cannot be described in terms of a percolation model, as opposed to the suggested correspondence for eigenvectors of 2 dimensional manifolds.Comment: 28 pages, 11 figure

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.Peer reviewe

Alive but Barely Kicking: News from 3+ yr of Swift and XMM-Newton X-Ray Monitoring of Quasiperiodic Eruptions from eRO-QPE1

Quasiperiodic eruptions (QPEs) represent a novel class of extragalactic X-ray transients that are known to repeat at roughly regular intervals of a few hours to days. Their underlying physical mechanism is a topic of heated debate, with most models proposing that they originate either from instabilities within the inner accretion flow or from orbiting objects. At present, our knowledge of how QPEs evolve over an extended timescale of multiple years is limited, except for the unique QPE source GSN 069. In this study, we present results from strategically designed Swift observing programs spanning the past 3 yr, aimed at tracking eruptions from eRO-QPE1. Our main results are as follows: (1) the recurrence time of eruptions can vary from flare to flare and is in the range of 0.6–1.2 days; (2) there is no detectable secular trend in evolution of the recurrence times; (3) consistent with prior studies, their eruption profiles can have complex shapes; and (4) the peak flux of the eruptions has been declining over the past 3 yr, with the eruptions barely detected in the most recent Swift data set taken in 2023 June. This trend of weakening eruptions has been reported recently in GSN 069. However, because the background luminosity of eRO-QPE1 is below our detection limit, we cannot verify whether the weakening is correlated with the background luminosity (as is claimed to be the case for GSN 069). We discuss these findings within the context of various proposed QPE models

The DEAD-box RNA Helicase DDX6 is Required for Efficient Encapsidation of a Retroviral Genome

Viruses have to encapsidate their own genomes during the assembly process. For most RNA viruses, there are sequences within the viral RNA and virion proteins needed for high efficiency of genome encapsidation. However, the roles of host proteins in this process are not understood. Here we find that the cellular DEAD-box RNA helicase DDX6 is required for efficient genome packaging of foamy virus, a spumaretrovirus. After infection, a significant amount of DDX6, normally concentrated in P bodies and stress granules, re-localizes to the pericentriolar site where viral RNAs and Gag capsid proteins are concentrated and capsids are assembled. Knockdown of DDX6 by siRNA leads to a decreased level of viral nucleic acids in extracellular particles, although viral protein expression, capsid assembly and release, and accumulation of viral RNA and Gag protein at the assembly site are little affected. DDX6 does not interact stably with Gag proteins nor is it incorporated into particles. However, we find that the ATPase/helicase motif of DDX6 is essential for viral replication. This suggests that the ATP hydrolysis and/or the RNA unwinding activities of DDX6 function in moderating the viral RNA conformation and/or viral RNA-Gag ribonucleoprotein complex in a transient manner to facilitate incorporation of the viral RNA into particles. These results reveal a unique role for a highly conserved cellular protein of RNA metabolism in specifically re-locating to the site of viral assembly for its function as a catalyst in retroviral RNA packaging

Frequent and Recent Human Acquisition of Simian Foamy Viruses Through Apes' Bites in Central Africa

Human infection by simian foamy viruses (SFV) can be acquired by persons occupationally exposed to non-human primates (NHP) or in natural settings. This study aimed at getting better knowledge on SFV transmission dynamics, risk factors for such a zoonotic infection and, searching for intra-familial dissemination and the level of peripheral blood (pro)viral loads in infected individuals. We studied 1,321 people from the general adult population (mean age 49 yrs, 640 women and 681 men) and 198 individuals, mostly men, all of whom had encountered a NHP with a resulting bite or scratch. All of these, either Pygmies (436) or Bantus (1085) live in villages in South Cameroon. A specific SFV Western blot was used and two nested PCRs (polymerase, and LTR) were done on all the positive/borderline samples by serology. In the general population, 2/1,321 (0.2%) persons were found to be infected. In the second group, 37/198 (18.6%) persons were SFV positive. They were mostly infected by apes (37/39) FV (mainly gorilla). Infection by monkey FV was less frequent (2/39). The viral origin of the amplified sequences matched with the history reported by the hunters, most of which (83%) are aged 20 to 40 years and acquired the infection during the last twenty years. The (pro)viral load in 33 individuals infected by a gorilla FV was quite low (<1 to 145 copies per 105 cells) in the peripheral blood leucocytes. Of the 30 wives and 12 children from families of FV infected persons, only one woman was seropositive in WB without subsequent viral DNA amplification. We demonstrate a high level of recent transmission of SFVs to humans in natural settings specifically following severe gorilla bites during hunting activities. The virus was found to persist over several years, with low SFV loads in infected persons. Secondary transmission remains an open question

On Eigenvalues of Random Complexes

We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$ vertices. We show that for $p=\Omega(\log n/n)$, the eigenvalues of these matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of Garland, are arguments that relate the eigenvalues of these matrices to those of graphs that arise as links of $(k-2)$-dimensional faces. Garland's result concerns the Laplacian; we develop an analogous result for the adjacency matrix. The same arguments apply to other models of random complexes which allow for dependencies between the choices of $k$-dimensional simplices. In the second part of the paper, we apply this to the question of possible higher-dimensional analogues of the discrete Cheeger inequality, which in the classical case of graphs relates the eigenvalues of a graph and its edge expansion. It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the higher-dimensional Laplacian spectra capture the notion of coboundary expansion - a generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov. We show that this most straightforward version of a higher-dimensional discrete Cheeger inequality fails, in quite a strong way: For every $k\geq 2$ and $n\in \mathbb{N}$, there is a $k$-dimensional complex $Y^k_n$ on $n$ vertices that has strong spectral expansion properties (all nontrivial eigenvalues of the normalised $k$-dimensional Laplacian lie in the interval $[1-O(1/\sqrt{n}),1+O(1/\sqrt{n})]$) but whose coboundary expansion is bounded from above by $O(\log n/n)$ and so tends to zero as $n\rightarrow \infty$; moreover, $Y^k_n$ can be taken to have vanishing integer homology in dimension less than $k$.Comment: Extended full version of an extended abstract that appeared at SoCG 2012, to appear in Israel Journal of Mathematic