Purifying noisy entanglement requires collective measurements

Known entanglement purification protocols for mixed states use collective measurements on several copies of the state in order to increase the entanglement of some of them. We address the question of whether it is possible to purify the entanglement of a state by processing each copy separately. While this is possible for pure states, we show that this is impossible, in general, for mixed states. The importance of this result both conceptually and for experimental realization of purification is discussed. We also give explicit invariants of an entangled state of two qubits under local actions and classical communication.Comment: 5 pages, Late

Bound Entanglement and Teleportation

Recently M. Horodecki, P. Horodecki and R. Horodecki have introduced a set of density matrices of two spin-1 particles from which it is not possible to distill any maximally entangled states, even though the density matrices are entangled. Thus these density matrices do not allow reliable teleportation. However it might nevertheless be the case that these states can be used for teleportation, not reliably, but still with fidelity greater than that which may be achieved with a classical scheme. We show that, at least for some of these density matrices, teleportation cannot be achieved with better than classical fidelity.Comment: 3 pages, RevTe

The biomechanical effects of the inclusion of a torque absorber and type of knee units on trans-femoral amputee gait

This paper reports on a pilot study investigating the effects on the gait of two transfemoral amputees of to the inclusion of a torque absorber (TA) and its location relative to the knee unit. Both subjects carried out gait tests with a prosthesis with no TA with, a TA proximal to the knee unit and with a TA distal to the knee unit. Three-dimensional gait analysis was carried out to establish the kinematic and kinetic gait parameters of both the prosthetic and sound side. It was found that the TA did not significantly affect the sagittal kinetic and kinematic parameters of the sound or the prosthetic side. However, for one subject the axial rotation of the socket relative to the foot was significantly greater with the TA. It was concluded that by using the methodology of this pilot study, it is possible to investigate the rotations in the transverse plane within the prosthetic limb and pelvis. Further, including a TA may reduce the relative motion between the stump and the socket and therefore may decrease skin breakdown due to diminished shear force

Non-local properties of multi-particle density matrices

As far as entanglement is concerned, two density matrices of $n$ particles are equivalent if they are on the same orbit of the group of local unitary transformations, $U(d_1)\times...\times U(d_n)$ (where the Hilbert space of particle $r$ has dimension $d_r$). We show that for $n$ greater than or equal to two, the number of independent parameters needed to specify an $n$-particle density matrix up to equivalence is $\Pi_r d_r^2 - \sum_r d_r^2 + n - 1$. For $n$ spin-${1\over 2}$ particles we also show how to characterise generic orbits, both by giving an explicit parametrisation of the orbits and by finding a finite set of polynomial invariants which separate the orbits.Comment: 13 pages RevTe

Cross-country comparison of the replacement incentives of the EU ETS in 2008-12: the case of the power sector

In this paper, we conduct a cross-country quantitative analysis of the replacement incentives generated by the EU ETS for the power sector in 2008-12. In order to do so, the allocation rules of the Member States are applied to concrete reference power plants for three different fuel types (lignite, hard coal and gas). Based on these calculations, we compare installation-specific replacement in-centives across the Member States. Our analysis shows that replacement incentives vary significantly across Member States and typically deviate from the incentives provided in the reference case of full auctioning. Furthermore, the EU ETS allocation rules lead to perverse incentives in approximately 30% of the possible replacement options. Only 5 MS do not provide any perverse incentives. Finally, we explore the link between replacement incentives and allocation types. Based on our findings, we derive policy recommendations for the design of emission trading schemes emerging around the world. --EU emission trading scheme (EU ETS),replacement,adoption,diffusion,power sector,allocation rules

Bell inequalities for arbitrarily high dimensional systems

We develop a novel approach to Bell inequalities based on a constraint that the correlations exhibited by local realistic theories must satisfy. This is used to construct a family of Bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise. In particular our work gives an analytic description of numerical results of D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski, A. Zeilinger, Phys. Rev. Lett. {\bf 85}, 4418 (2000) and T. Durt, D. Kaszlikowski, M. Zukowski, quant-ph/0101084, and generalises them to arbitrarily high dimensionality.Comment: 6 pages, late

The Extent of Multi-particle Quantum Non-locality

It is well known that entangled quantum states can be nonlocal: the correlations between local measurements carried out on these states cannot always be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are even more nonlocal than bipartite ones in the sense that nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalises work of Svetlichny and others in which it was shown that a particular class of classical nonlocal models, the ``separable'' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition.Comment: 10 pages, 2 figures, journal versio

Interferometric near-field characterization of plasmonic slot waveguides in single- and poly-crystalline gold films

Plasmonic waveguides are a promising platform for integrated nanophotonic circuits and nanoscale quantum optics. Their use is however often hampered by the limited propagation length of the guided surface plasmon modes. A detailed understanding of the influence of the material quality and the waveguide geometry on the complex mode index is therefore crucial. In this letter, we present interferometric near-field measurements at telecommunication wavelength on plasmonic slot waveguides fabricated by focused ion beam milling in single- and poly-crystalline gold films. We observe a significantly better performance of the slot waveguides in the single-crystalline gold film for slot widths below $100\,\mathrm{nm}$. In contrast for larger slot widths, both gold films give rise to comparable mode propagation lengths. Our experimental observations indicate that the nature of the dominant loss channel changes with increasing gap size from Ohmic to leakage radiation. Our experimental findings are reproduced by three dimensional numerical calculations.Comment: 4 figure