Optimum unambiguous identification of d unknown pure qudit states

We address the problem of unambiguously identifying the state of a probe qudit with the state of one of d reference qudits. The reference states are assumed pure and linearly independent but we have no knowledge of them. The state of the probe qudit is assumed to coincide equally likely with either one of the d unknown reference states. We derive the optimum measurement strategy that maximizes the success probability of unambiguous identification and find that the optimum strategy is a generalized measurement. We give both the measurement operators and the optimum success probability explicitly. Technically, the problem we solve amounts to the optimum unambiguous discrimination of d known mixed quantum states.Comment: A reference has been included and a sign error has been corrected that propagated and affected the final result and is unfortunately also present in the printed journal versio

Compactification of a map which is mapped to itself

We prove that if $T: X \to X$ is a selfmap of a set $X$ such that \bigcap \{T^{n}X: n\in N}\} is a one-point set, then the set $X$ can be endowed with a compact Hausdorff topology so that $T$ is continuous.Comment: 5 page

Detecting Wage Under-reporting Using a Double Hurdle Model

We estimate a double hurdle (DH) model of the Hungarian wage distribution assuming censoring at the minimum wage and wage under-reporting (i.e. compensation consisting of the minimum wage, subject to taxation, and an unreported cash supplement). We estimate the probability of under-reporting for minimum wage earners, simulate their genuine earnings and classify them and their employers as 'cheaters' and 'non-cheaters'. In the possession of the classification we check how cheaters and non-cheaters reacted to the introduction of a minimum social security contribution base, equal to 200 per cent of the minimum wage, in 2007. The findings suggest that cheaters were more likely to raise the wages of their minimum wage earners to 200 per cent of the minimum wage thereby reducing the risk of tax audit. Cheating firms also experienced faster average wage growth and slower output growth. The results suggest that the DH model is able to identify the loci of wage under-reporting with some precision.tax evasion, double hurdle model, Hungary