Statistical bounds on the dynamical production of entanglement

We present a random-matrix analysis of the entangling power of a unitary operator as a function of the number of times it is iterated. We consider unitaries belonging to the circular ensembles of random matrices (CUE or COE) applied to random (real or complex) non-entangled states. We verify numerically that the average entangling power is a monotonic decreasing function of time. The same behavior is observed for the "operator entanglement" --an alternative measure of the entangling strength of a unitary. On the analytical side we calculate the CUE operator entanglement and asymptotic values for the entangling power. We also provide a theoretical explanation of the time dependence in the CUE cases.Comment: preprint format, 14 pages, 2 figure

Sulphate-controlled Diversity of Subterranean Microbial Communities over Depth in Deep Groundwater with Opposing Gradients of Sulphate and Methane

The groundwater system in Olkiluoto, Finland, is stratified with a mixing layer at a depth of approximately 300m between sulphate-rich, methane-poor and sulphate-poor, methane-rich groundwaters. New sequence library data obtained by 454 pyrotag sequencing of the v4v6 16S rDNA region indicated that sulphate-reducing bacteria (SRB) dominated the mixing layer while SRB could not be detected in the deep sulphate-poor groundwater samples. With the indispensable support of the sequence data, it could be demonstrated that sulphate was the only component needed to trigger a very large community transition in deep sulphate-poor, methane-rich groundwater from a non-sulphate-reducing community comprising Hydrogenophaga, Pseudomonas, Thiobacillus, Fusibacter, and Lutibacter to a sulphate-reducing community with Desulfobacula, Desulfovibrio, Desufobulbaceae, Desulfobacterium, Desulfosporosinus, and Desulfotignum. Experiments with biofilms and planktonic microorganisms in flow cells under in situ conditions confirmed that adding sulphate to the sulphate-poor groundwater generated growth of cultivable SRB and detectable SRB-related sequences. It was also found that the 16S rDNA diversity of the biofilms was conserved over 103 d and that there was great similarity in diversity between the microorganisms in the biofilms and in the flowing groundwater. This work demonstrates that the presence/absence of only one geochemical parameter, i.e., sulphate, in the groundwater significantly influenced the diversity of the investigated subterranean microbial community

2-Form Gravity of the Lorentzian Signature

We introduce a new spinorial, BF-like action for the Einstein gravity. This is a first, up to our knowledge, 2-form action which describes the real, Lorentzian gravity and uses only the self-dual connection. In the generic case, the corresponding classical canonical theory is equivalent to the Einstein-Ashtekar theory plus the reality conditions

Distribution of G-concurrence of random pure states

Average entanglement of random pure states of an N x N composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant we characterize the probability distribution P(D). Similar results are obtained for the rescaled N-th root of the determinant, called G-concurrence. We show that in the limit $N\to\infty$ this quantity becomes concentrated at a single point G=1/e. The position of the concentration point changes if one consider an arbitrary N x K bipartite system, in the joint limit $N,K\to\infty$, K/N fixed.Comment: RevTeX4, 11 pages, 4 Encapsuled PostScript figures - Introduced new results, Section II and V have been significantly improved - To appear on PR

Practical recommendations for measuring rates of visual field change in glaucoma

To date, there has been a lack of evidence-based guidance on the frequency of visual field examinations required to identify clinically meaningful rates of change in glaucoma. The objective of this perspective is to provide practical recommendations for this purpose. The primary emphasis is on the period of time and number of examinations required to measure various rates of change in mean deviation (MD) with adequate statistical power. Empirical data were used to obtain variability estimates of MD while statistical modelling techniques derived the required time periods to detect change with various degrees of visual field variability. We provide the frequency of examinations per year required to detect different amounts of change in 2, 3 and 5 years. For instance, three examinations per year are required to identify an overall change in MD of 4 dB over 2 years in a patient with average visual field variability. Recommendations on other issues such as examination type, strategy and quality are also made

Structural approximations to positive maps and entanglement breaking channels

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.Comment: 18 pages, 3 figure

Atmospheric predictability revisited

This article examines the potential to improve numerical weather prediction (NWP) by estimating upper and lower bounds on predictability by re-visiting the original study of Lorenz (1982) but applied to the most recent version of the European Centre for Medium Range Weather Forecasts (ECMWF) forecast system, for both the deterministic and ensemble prediction systems (EPS). These bounds are contrasted with an older version of the same NWP system to see how they have changed with improvements to the NWP system. The computations were performed for the earlier seasons of DJF 1985/1986 and JJA 1986 and the later seasons of DJF 2010/2011 and JJA 2011 using the 500-hPa geopotential height field. Results indicate that for this field, we may be approaching the limit of deterministic forecasting so that further improvements might only be obtained by improving the initial state. The results also show that predictability calculations with earlier versions of the model may overestimate potential forecast skill, which may be due to insufficient internal variability in the model and because recent versions of the model are more realistic in representing the true atmospheric evolution. The same methodology is applied to the EPS to calculate upper and lower bounds of predictability of the ensemble mean forecast in order to explore how ensemble forecasting could extend the limits of the deterministic forecast. The results show that there is a large potential to improve the ensemble predictions, but for the increased predictability of the ensemble mean, there will be a trade-off in information as the forecasts will become increasingly smoothed with time. From around the 10-d forecast time, the ensemble mean begins to converge towards climatology. Until this point, the ensemble mean is able to predict the main features of the large-scale flow accurately and with high consistency from one forecast cycle to the next. By the 15-d forecast time, the ensemble mean has lost information with the anomaly of the flow strongly smoothed out. In contrast, the control forecast is much less consistent from run to run, but provides more detailed (unsmoothed) but less useful information

Why Don't We Have a Covariant Superstring Field Theory?

This talk deals with the old problem of formulatingn a covariant quantum theory of superstrings, ``covariant'' here meaning having manifest Lorentz symmetry and supersymmetry. The advantages and disadvantages of several quantization methods are reviewed. Special emphasis is put on the approaches using twistorial variables, and the algebraic structures of these. Some unsolved problems are identified.Comment: 5 pages, Goteborg-ITP-94-24, plain te

From SICs and MUBs to Eddington

This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.Comment: 12 pages; from the Festschrift for Tony Sudber

Measurements of Lifetimes and a Limit on the Lifetime Difference in the Neutral D-Meson System

Using the large hadroproduced charm sample collected in experiment E791 at Fermilab, we report the first directly measured constraint on the decay-width difference Delta Gamma for the mass eigenstates of the D0-D0bar system. We obtain our result from lifetime measurements of the decays D0 --> K-pi+ and D0 --> K-K+, under the assumption of CP invariance, which implies that the CP eigenstates and the mass eigenstates are the same. The lifetime of D0 --> K-K+ (the CP-even final state is \tau_KK = 0.410 +/- 0.011 +/- 0.006 ps, and the lifetime of D0 --> K-pi+ (an equal mixture of CP-odd and CP-even final states is tau_Kpi = 0.413 +/- 0.003 +/- 0.004 ps. The decay-width difference is Delta Gamma = 2(Gamma_KK - Gamma_Kpi) = 0.04 +/- 0.14 +/- 0.05 ps^-1. We relate these measurements to measurements of mixing in the neutral D-meson system.Comment: 8 pages + 3 figures + 2 table