On the geometry of entangled states

The basic question that is addressed in this paper is finding the closest separable state for a given entangled state, measured with the Hilbert Schmidt distance. While this problem is in general very hard, we show that the following strongly related problem can be solved: find the Hilbert Schmidt distance of an entangled state to the set of all partially transposed states. We prove that this latter distance can be expressed as a function of the negative eigenvalues of the partial transpose of the entangled state, and show how it is related to the distance of a state to the set of positive partially transposed states (PPT-states). We illustrate this by calculating the closest biseparable state to the W-state, and give a simple and very general proof for the fact that the set of W-type states is not of measure zero. Next we show that all surfaces with states whose partial transposes have constant minimal negative eigenvalue are similar to the boundary of PPT states. We illustrate this with some examples on bipartite qubit states, where contours of constant negativity are plotted on two-dimensional intersections of the complete state space.Comment: submitted to Journal of Modern Optic

Variational Characterisations of Separability and Entanglement of Formation

In this paper we develop a mathematical framework for the characterisation of separability and entanglement of formation (EoF) of general bipartite states. These characterisations are of the variational kind, meaning that separability and EoF are given in terms of a function which is to be minimized over the manifold of unitary matrices. A major benefit of such a characterisation is that it directly leads to a numerical procedure for calculating EoF. We present an efficient minimisation algorithm and an apply it to the bound entangled 3X3 Horodecki states; we show that their EoF is very low and that their distance to the set of separable states is also very low. Within the same variational framework we rephrase the results by Wootters (W. Wootters, Phys. Rev. Lett. 80, 2245 (1998)) on EoF for 2X2 states and present progress in generalising these results to higher dimensional systems.Comment: 11 pages RevTeX, 4 figure

N-representability is QMA-complete

We study the computational complexity of the N-representability problem in quantum chemistry. We show that this problem is QMA-complete, which is the quantum generalization of NP-complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that reduces the problem of finding ground states to N-representability

Growth kinetics of environmental Legionella pneumophila isolated from industrial wastewater

Wastewater treatment plants are environmental niches for Legionella pneumophila, the most commonly identified causative agent of severe pneumonia known as Legionnaire's disease. In the present study, Legionella pneumophila's concentrations were monitored in an industrial wastewater treatment plant and environmental isolates were characterized concerning their growth kinetics with respect to temperature and their inhibition by organic acids and ammonium. The results of the monitoring study showed that Legionella pneumophila occurs in activated sludge tanks operated with very different sludge retention times, 2.5 days in a complete-mix reactor, and 10 days in a membrane bioreactor, indicating that this bacterium can grow at different rates, despite the same wastewater temperature of 35 degrees C. The morphology of Legionella cells is different in both reactors; in the membrane bioreactor, the bacteria grow in clusters, while in the complete-mix reactor, filaments predominate demonstrating a faster growth rate. Legionella pneumophila concentrations in the complete-mix reactor and in the membrane bioreactor were within the range 3 x 10(1) to 4.8 x 10(3) GU/mL and 3 x 10(2) to 4.7 x 10(3) GU/mL, respectively. Environmental Legionella pneumophila SG2-14 isolates showed distinct temperature preferences. The lowest growth rate was observed at 28 degrees C, and the highest 0.34 d(-1) was obtained at 42 degrees C. The presence of high concentrations of organic acids and ammonium found in anaerobically pre-treated wastewater caused growth inhibition. Despite the increasing research efforts, the mechanisms governing the growth of Legionella pneumophila in wastewater treatment plants are still unclear. New innovative strategies to prevent the proliferation of this bacterium in wastewater are in demand

Quantum Metropolis Sampling

The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is believed to be intractable for classical computers. Such a machine would have a wide range of applications in the simulation of many-body quantum physics, including condensed matter physics, chemistry, and high energy physics. Part of Feynman's challenge was met by Lloyd who showed how to approximately decompose the time-evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that basically acquired a monopoly for the simulation of interacting particles. Here, we demonstrate how to implement a quantum version of the Metropolis algorithm on a quantum computer. This algorithm permits to sample directly from the eigenstates of the Hamiltonian and thus evades the sign problem present in classical simulations. A small scale implementation of this algorithm can already be achieved with today's technologyComment: revised versio

Osteochondroma of the proximal humerus with frictional bursitis and secondary synovial osteochondromatosis

We report a case of multiple hereditary exostosis in a 33-year old patient with clinical symptoms of pain and impression of a growing mass of the left shoulder alerting potential risk of malignant transformation of an osteochondroma. Imaging studies illustrated perilesional bursitis surrounding an osteochondroma of the proximal humerus. Malignant transformation was excluded with MRI. Fragments of the osteochondroma were dislocated in the inflammatory synovial bursa illustrating a case of secondary synovial osteochondromatosis

Enterohemorrhagic Escherichia coli with particular attention to the German outbreak strain O104:H4

This review deals with the epidemiology and ecology of enterohemorrhagic Escherichia coli (EHEC), a subset of the verocytotoxigenic Escherichia coli (VTEC), and subsequently discusses its public health concern. Attention is also given to the outbreak strain O104:H4, which has been isolated as causative agent of the second largest outbreak of the hemolytic uremic syndrome worldwide, which started in Germany in May 2011. This outbreak strain is not an EHEC as such but possesses an unusual combination of EHEC and enteroaggregative E. coli (EAggEC) virulence properties

Functionality in single-molecule devices: Model calculations and applications of the inelastic electron tunneling signal in molecular junctions

We analyze how functionality could be obtained within single-molecule devices by using a combination of non-equilibrium Green's functions and ab-initio calculations to study the inelastic transport properties of single-molecule junctions. First we apply a full non-equilibrium Green's function technique to a model system with electron-vibration coupling. We show that the features in the inelastic electron tunneling spectra (IETS) of the molecular junctions are virtually independent of the nature of the molecule-lead contacts. Since the contacts are not easily reproducible from one device to another, this is a very useful property. The IETS signal is much more robust versus modifications at the contacts and hence can be used to build functional nanodevices. Second, we consider a realistic model of a organic conjugated molecule. We use ab-initio calculations to study how the vibronic properties of the molecule can be controlled by an external electric field which acts as a gate voltage. The control, through the gate voltage, of the vibron frequencies and (more importantly) of the electron-vibron coupling enables the construction of functionality: non-linear amplification and/or switching is obtained from the IETS signal within a single-molecule device.Comment: Accepted for publication in Journal of Chemical Physic

Binegativity and geometry of entangled states in two qubits

We prove that the binegativity is always positive for any two-qubit state. As a result, as suggested by the previous works, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the PPT-entanglement cost for any two-qubit state is determined to be the logarithmic negativity of the state. Further, the proof reveals some geometrical characteristics of the entangled states, and shows that the partial transposition can give another separable approximation of the entangled state in two qubits.Comment: 5 pages, 3 figures. I made the proof more transparen