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

Resonance energy transfer: The unified theory revisited

Resonanceenergy transfer (RET) is the principal mechanism for the intermolecular or intramolecular redistribution of electronic energy following molecular excitation. In terms of fundamental quantum interactions, the process is properly described in terms of a virtual photon transit between the pre-excited donor and a lower energy (usually ground-state) acceptor. The detailed quantum amplitude for RET is calculated by molecular quantum electrodynamical techniques with the observable, the transfer rate, derived via application of the Fermi golden rule. In the treatment reported here, recently devised state-sequence techniques and a novel calculational protocol is applied to RET and shown to circumvent problems associated with the usual method. The second-rank tensor describing virtual photon behavior evolves from a Green’s function solution to the Helmholtz equation, and special functions are employed to realize the coupling tensor. The method is used to derive a new result for energy transfer systems sensitive to both magnetic- and electric-dipole transitions. The ensuing result is compared to that of pure electric-dipole–electric-dipole coupling and is analyzed with regard to acceptable transfer separations. Systems are proposed where the electric-dipole–magnetic-dipole term is the leading contribution to the overall rate

BMO spaces associated with semigroups of operators

We study BMO spaces associated with semigroup of operators and apply the results to boundedness of Fourier multipliers. We prove a universal interpolation theorem for BMO spaces and prove the boundedness of a class of Fourier multipliers on noncommutative Lp spaces for all 1 < p < \infty, with optimal constants in p.Comment: Math An

Joint system quantum descriptions arising from local quantumness

Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely

Nitrogen-Enriched Graphene Iron Oxide Nanoparticles as Innovative Catalysts: First Application to Cyclopropanation Reactions

A new class of catalysts having a metal/metal oxide core surrounded by a few nitrogen-enriched graphene layers (NGR) has recently brought immense attention in research. Until now, NGR catalysts have mostly been employed for hydrogenation reactions. In this work, we expand the field of applicability of NGR catalysts to cyclopropanation reactions. The activity of Fe2O3/NGr@C has been studied by using ethyl diazoacetate and \u3b1-methylstyrene as substrates. Various parameters such as solvents, temperature and time were changed. Fe2O3/NGr@C-catalysts showed best activity in dimethoxyethane at 60 oC, affording high yields of the desired cyclopropanes (mixture of cis and trans isomers) and only 1-2 % of ethyl maleate and fumarate (Figure 1). The catalyst gradually deactivates after each recycle, but we were able to reactivate the recovered catalyst by treating it with dilute H2O2 (1:10 with distilled water). Like \u3b1-methylstyrene, several olefins such as 4-chloro-\u3b1-methyl styrene, 4-methylstyrene, 2- methylstyrene, 3-methylstyrene, 4-chlorostyrene, 4-t-butylstyrene, 1-octene etc. have been tested in order to explore the substrate scope. The corresponding cyclopropanes were obtained in high to excellent isolated yields (84-98%). In all cases trans diastereoselectivity was found, but even the minor cis isomer could be isolated in a pure form

Iron/N-doped graphene nano-structured catalysts for general cyclopropanation of olefins

The first examples of heterogeneous Fe-catalysed cyclopropanation reactions are presented. Pyrolysis of in situ-generated iron/phenanthroline complexes in the presence of a carbonaceous material leads to specific supported nanosized iron particles, which are effective catalysts for carbene transfer reactions. Using olefins as substrates, cyclopropanes are obtained in high yields and moderate diastereoselectivities. The developed protocol is scalable and the activity of the recycled catalyst after deactivation can be effectively restored using an oxidative reactivation protocol under mild conditions

Generation and Handling of Hard Drive Duplicates as Piece of Evidence

An important area in digital forensics is images of hard disks. The correct production of the images as well as the integrity and authenticity of each hard disk image is essential for the probative force of the image to be used at court. Integrity and authenticity are under suspicion as digital evidence is stored and used by software based systems. Modifications to digital objects are hard or even impossible to track and can occur even accidentally. Even worse, vulnerabilities occur for all current computing systems. Therefore, it is difficult to guarantee a secure environment for forensic investigations. But intended deletions of dedicated data of disk images are often required because of legal issues in many countries. This article provides a technical framework on the protection of the probative force of hard disk images by ensuring the integrity and authenticity using state of the art technology. It combines hardware-based security, cryptographic hash functions and digital signatures to achieve a continuous protection of the image together with a reliable documentation of the status of the device that was used for image creation. The framework presented allows to detect modifications and to pinpoint the exact area of the modification to the digital evidence protecting the probative force of the evidence at a whole. In addition, it also supports the deletion of parts of images without invalidating the retained data blocks. Keywords: digital evidence, probative force hard disk image, verifiable deletion of image data, trusted imaging softwar