Connes' embedding problem and Tsirelson's problem

We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting C*-algebras. Connes' embedding problem asks whether any separable II$_1$ factor is a subfactor of the ultrapower of the hyperfinite II$_1$ factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely, a positve answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem

An Assessment of the Effect of Budgetary Practices on Performance of Public Secondary Schools in Nakuru Municipality

Amid the need to foster efficiency and effectiveness in schools, budgetary practices have been embraced by public secondary schools in Kenya.  Key of which is to compel planning and to provide performance measurement criteria. Therefore, this study sought to assess the effect of budgetary practices on the performance of public secondary schools in the Nakuru Municipality. The study conducted a survey involving two respondents from each of the 22 public secondary schools in Nakuru Municipality. A structured questionnaire was used to collect primary data. The results of the study indicated that budgetary practices had a strong positive effect on the performance of public secondary schools. Keywords: Budgetary practices, performance of public secondary schools, Nakuru Municipality

Analysis of vertebral chemistry to assess stock structure in a deep-sea shark, Etmopterus spinax

First published online: October 27, 2016Deep-sea sharks play a valuable ecological role helping maintain food web balance, yet they are vulnerable to commercial fishing because of slow growth rates and low reproductive capacity. Overfishing of sharks can heavily impact marine ecosystems and the fisheries these support. Knowledge of stock structure is integral to sustainable management of fisheries. The present study analysed vertebral chemistry using laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) to assay concentrations of 7Li, 23Na, 24Mg, 55Mn, 59Co, 60Ni, 63Cu, 66Zn, 85Rb, 88Sr, 138Ba and 208Pb to assess stock structure in a deep-sea shark, Etmopterus spinax, in Norwegian and French waters. Few studies have applied this technique to elasmobranch vertebrae and the present study represents its first application to a deep-sea shark. Three stocks were identified at the regional scale off western Norway, southern Norway, and France. At finer spatial scales there was evidence of strong population mixing. Overall, the general pattern of stock structure outlined herein provides some indication of the spatial scales at which stocks should be viewed as distinct fisheries management units. The identification of an effective multi-element signature for distinguishing E. spinax stocks utilizing Sr, Ba, Mg, Zn and Pb and the methodological groundwork laid in the present study could also expedite future research into stock structure for E. spinax and deep-sea elasmobranchs more generally.Matthew N. McMillan, Christopher Izzo, Claudia Junge, Ole Thomas Albert, Armelle Jung and Bronwyn M. Gillander

The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

Multiplicativity of completely bounded p-norms implies a new additivity result

We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the form gamma_{12} = (I \ot Phi)(| psi >< psi |). We show that this follows from multiplicativity of the completely bounded norm of Phi considered as a map from L_1 -> L_p for L_p spaces defined by the Schatten p-norm on matrices; we also give an independent proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L_1 -> L_p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.Comment: Final version for Commun. Math. Physics. Section 5.2 of previous version deleted in view of the results in quant-ph/0601071 Other changes mino

Experimental estimation of the dimension of classical and quantum systems

An overwhelming majority of experiments in classical and quantum physics make a priori assumptions about the dimension of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness answers this question, as it allows one to bound the dimension of an unknown classical or quantum system in a device-independent manner, that is, only from the statistics of measurements performed on it. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario. We use pairs of photons entangled in both polarization and orbital angular momentum to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our results open new avenues for the device-independent estimation of unknown quantum systems and for applications in quantum information science.Comment: See also similar, independent and jointly submitted work of J. Ahrens et al., quant-ph/1111.127

Analytical model of brittle destruction based on hypothesis of scale similarity

The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys the power law with the exponent between -4 and -1. The model of destruction has much in common with the fractal theory. The power exponent can be expressed in terms of the fractal dimension. Reasonable assumptions on the shape of fragments concretize the power exponent, and vice versa possible destruction laws can be inferred on the basis of measured size distributions.Comment: 10 pages, 3 figure

contact.engineering -- Create, analyze and publish digital surface twins from topography measurements across many scales

The optimization of surface finish to improve performance occurs largely through trial and error, despite significant advancements in the relevant science. There are three central challenges that account for this disconnect: (1) the challenge of integration of many different types of measurement for the same surface to capture the multi-scale nature of roughness; (2) the technical complexity of implementing spectral analysis methods, and of applying mechanical or numerical models to describe surface performance; (3) a lack of consistency between researchers and industries in how surfaces are measured, quantified, and communicated. Here we present a freely-available internet-based application which attempts to overcome all three challenges. First, the application enables the user to upload many different topography measurements taken from a single surface, including using different techniques, and then integrates all of them together to create a digital surface twin. Second, the application calculates many of the commonly used topography metrics, such as root-mean-square parameters, power spectral density (PSD), and autocorrelation function (ACF), as well as implementing analytical and numerical calculations, such as boundary element modeling (BEM) for elastic and plastic deformation. Third, the application serves as a repository for users to securely store surfaces, and if they choose, to share these with collaborators or even publish them (with a digital object identifier) for all to access. The primary goal of this application is to enable researchers and manufacturers to quickly and easily apply cutting-edge tools for the characterization and properties-modeling of real-world surfaces. An additional goal is to advance the use of open-science principles in surface engineering by providing a FAIR database where researchers can choose to publish surface measurements for all to use.Comment: 19 pages, 6 figure