The distillability problem revisited

An important open problem in quantum information theory is the question of the existence of NPT bound entanglement. In the past years, little progress has been made, mainly because of the lack of mathematical tools to address the problem. (i) In an attempt to overcome this, we show how the distillability problem can be reformulated as a special instance of the separability problem, for which a large number of tools and techniques are available. (ii) Building up to this we also show how the problem can be formulated as a Schmidt number problem. (iii) A numerical method for detecting distillability is presented and strong evidence is given that all 1-copy undistillable Werner states are also 4-copy undistillable. (iv) The same method is used to estimate the volume of distillable states, and the results suggest that bound entanglement is primarily a phenomenon found in low dimensional quantum systems. (v) Finally, a set of one parameter states is presented which we conjecture to exhibit all forms of distillability.Comment: Several corrections, main results unchange

On independent permutation separability criteria

Recently P. Wocjan and M. Horodecki [quant-ph/0503129] gave a characterization of combinatorially independent permutation separability criteria. Combinatorial independence is a necessary condition for permutations to yield truly independent criteria meaning that that no criterion is strictly stronger that any other. In this paper we observe that some of these criteria are still dependent and analyze why these dependencies occur. To remove them we introduce an improved necessary condition and give a complete classification of the remaining permutations. We conjecture that the remaining class of criteria only contains truly independent permutation separability criteria. Our conjecture is based on the proof that for two, three and four parties all these criteria are truly independent and on numerical verification of their independence for up to 8 parties. It was commonly believed that for three parties there were 9 independent criteria, here we prove that there are exactly 6 independent criteria for three parties and 22 for four parties.Comment: Revtex4, 7 pages, minor correction

Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory

PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review chapters on entanglement and distillation.Comment: 192 page

The disentangling power of unitaries

We define the disentangling power of a unitary operator in a similar way as the entangling power defined by Zanardi et al. [P. Zanardi, C. Zalka, L. Faoro, Phys. Rev. A 62 (2000) 030301(R), quant-ph/0005031]. A general formula is derived and it is shown that both quantities are directly proportional. All results concerning the entangling power can simply be translated into similar statements for the disentangling power. In particular, the disentangling power is maximal for certain permutations derived from orthogonal Latin squares. These permutations can therefore be interpreted as those that distort entanglement in a maximal way

Characterization of distillability of entanglement in terms of positive maps

A necessary and sufficient condition for 1-distillability is formulated in terms of decomposable positive maps. As an application we provide insight into why all states violating the reduction criterion map are distillable and demonstrate how to construct such maps in a systematic way. We establish a connection between a number of existing results, which leads to an elementary proof for the characterisation of distillability in terms of 2-positive maps.Comment: 4 pages, revtex4. Published revised version, title changed, expanded discussion, main result unchange

A (5,5) and (6,6) PPT edge state

Entangled states with a positive partial transpose (PPTES) have interest both in quantum information and in the theory of positive maps. In $3\otimes 3$ there is a conjecture by Sanpera, Bru{\ss} and Lewenstein [PRA, 63, 050301] that all PPTES have Schmidt number two (or equivalently that every 2-positive map between $3\times 3$ matrices is decomposable). In order to prove or disprove the conjecture it is sufficient to look at edge PPTES. Here the rank m of the PPTES and the rank n of its partial transpose seem to play an important role. Until recently all known examples of edge PPTES had ranks (4,4) or (6,7). In a recent paper Ha and Kye [quant-ph/0509079] managed to find edge PPTES for all ranks except (5,5) and (6,6). Here we complement their work and present edge PPTES with those ranks.Comment: 5 pages, comments welcom

H216O and HDO measurements with IASI/MetOp

International audienceIn this paper we analyze distributions of water vapour isotopologues in the troposphere using infrared spectra recorded by the Infrared Atmospheric Sounding Interferometer (IASI), which operates onboard the Metop satellite in nadir geometry. The simultaneous uncorrelated retrievals of H216O and HDO are performed on radiance measurements using a line-by-line radiative transfer model and an inversion procedure based on the Optimal Estimation Method (OEM). The characterizations of the retrieved products in terms of vertical sensitivity and error budgets show that IASI measurements contain up to 6 independent pieces of information on the vertical distribution of H216O and up to 3.5 for HDO from the surface up to the upper troposphere (0–20 km). Although the purpose of the paper is not validation, a restricted comparison with sonde measurements shows that the retrieved H216O profiles capture the seasonal/latitudinal variations of the water content, with good accuracy in the lowest layer but with larger uncertainties higher in the free and upper troposphere. Our results then demonstrate the ability of the IASI instrument to monitor atmospheric isotopologic water vapour distributions and to provide information on the partitioning of HDO as compared to H216O. The derivation of the δD is challenging and associated with large errors in the uncorrelated retrieval approach chosen here. As a result averaging on the vertical to produce a column-averaged δD is required to produce meaningful results for geophysical interpretation. As a case study, we analyse concentration distributions and spatio-temporal variations of H216O and δD during the October 2007 Krosa super-typhoon over South-East Asia. We show that individual δD have uncertainties of 37‰ for the vertically averaged values. Using the latter, we suggest that the typhoon produces a so-called amount-effect, where the δD is negatively correlated to the water amounts as a result of intense depletion of the deuterated species

Constraining industrial ammonia emissions using hyperspectral infrared imaging

Atmospheric emissions of reactive nitrogen in the form of nitrogen dioxide (NO) and ammonia (NH) worsen air quality and upon deposition, dramatically affect the environment. Recent infrared satellite measurements have revealed that NH emitted by industries are an important and underestimated emission source. Yet, to assess these emissions, current satellite sounders are severely limited by their spatial resolution. In this paper, we analyse measurement data recorded in a series of imaging surveys that were conducted over industries in the Greater Berlin area (Germany). On board the aircraft were the Telops Hyper-Cam LW, targeting NH measurements in the longwave infrared at a resolution of 4 m and the SWING+ spectrometer targeting NO measurements in the UV–Vis at a resolution of 180 m. Two flights were carried out over German’s largest production facility of synthetic NH , urea and other fertilizers. In both cases, a large NH plume was observed originating from the factory. Using a Gaussian plume model to take into account plume rise and dispersion, coupled with well-established radiative transfer and inverse methods, we retrieve vertical column densities. From these, we calculate NH emission fluxes using the integrated mass enhancement and cross-sectional flux methods, yielding consistent emissions of the order of 2200 t yr−1 for both flights, assuming constant fluxes across the year. These estimates are about five times larger than those reported in the European Pollutant Release and Transfer Register (E-PRTR) for this plant. In the second campaign, a co-emitted NO plume was measured, likely related to the production of nitric acid at the plant. A third flight was carried out over an area comprising the cities of Staßfurt and Bernburg. Several small NH plumes were seen, one over a production facility of mineral wool insulation, one over a sugar factory and two over the soda ash plants in Staßfurt and Bernburg. A fifth and much larger plume was seen to originate from the sedimentation basins associated with the soda ash plant in Staßfurt, indicating rapid volatilization of ammonium rich effluents. We use the different measurement campaigns to simulate measurements of Nitrosat, a potential future satellite sounder dedicated to the sounding of reactive nitrogen at a resolution of 500 m. We demonstrate that such measurements would allow accurately constraining emissions in a single overpass, overcoming a number of important drawbacks of current satellite sounders

Schmidt balls around the identity

Robustness measures as introduced by Vidal and Tarrach [PRA, 59, 141-155] quantify the extent to which entangled states remain entangled under mixing. Analogously, we introduce here the Schmidt robustness and the random Schmidt robustness. The latter notion is closely related to the construction of Schmidt balls around the identity. We analyse the situation for pure states and provide non-trivial upper and lower bounds. Upper bounds to the random Schmidt-2 robustness allow us to construct a particularly simple distillability criterion. We present two conjectures, the first one is related to the radius of inner balls around the identity in the convex set of Schmidt number n-states. We also conjecture a class of optimal Schmidt witnesses for pure states.Comment: 7 pages, 1 figur