Can the states of the W-class be suitable for teleportation

Entangled states of the W-class are considered as a quantum channel for teleportation or the states to be sent. The protocols have been found by unitary transformation of the schemes, based on the multiuser GHZ channel. The main feature of the W-quantum channels is a set of non-local operators, that allow receivers recovering unknown state.Comment: 4 pages, revtex4, no figure

On preparation of the W-states from atomic ensembles

A scheme, where three atomic ensembles can be prepared in the states of the W-class via Raman type interaction of strong classical field and a projection measurement involved three single-photon detectors and two beamsplitters, are considered. The obtained atomic entanglement consists of the Dicke or W-states of each of the ensembles.Comment: 4 pages, 1 figure, minor correction

Did Household Consumption Become More Volatile?

We show that volatility of household consumption, after accounting for predictable variation arising from movements in real interest rates, preferences and income shocks, increased between 1970 and 2002. For single parent households, and households headed by nonwhite or poorly educated individuals, this rise was signi¯cantly larger. This stands in sharp contrast with the dramatic fall in aggregate volatility of the US economy, and may have significant welfare implications. A spectacular fall in average covariances of consumption growth rates across households over this period accounts for the diverging paths of aggregate and household level volatilities.consumption risk, volatility decomposition, aggregate volatility, panel data.

Pitt's inequalities and uncertainty principle for generalized Fourier transform

We study the two-parameter family of unitary operators $$\mathcal{F}_{k,a}=\exp\Bigl(\frac{i\pi}{2a}\,(2\langle k\rangle+{d}+a-2 )\Bigr) \exp\Bigl(\frac{i\pi}{2a}\,\Delta_{k,a}\Bigr),$$ which are called $(k,a)$-generalized Fourier transforms and defined by the $a$-deformed Dunkl harmonic oscillator $\Delta_{k,a}=|x|^{2-a}\Delta_{k}-|x|^{a}$, $a>0$, where $\Delta_{k}$ is the Dunkl Laplacian. Particular cases of such operators are the Fourier and Dunkl transforms. The restriction of $\mathcal{F}_{k,a}$ to radial functions is given by the $a$-deformed Hankel transform $H_{\lambda,a}$. We obtain necessary and sufficient conditions for the weighted $(L^{p},L^{q})$ Pitt inequalities to hold for the $a$-deformed Hankel transform. Moreover, we prove two-sided Boas--Sagher type estimates for the general monotone functions. We also prove sharp Pitt's inequality for $\mathcal{F}_{k,a}$ transform in $L^{2}(\mathbb{R}^{d})$ with the corresponding weights. Finally, we establish the logarithmic uncertainty principle for $\mathcal{F}_{k,a}$.Comment: 16 page

On amplification of light in the continuous EPR state

Two schemes of amplification of two-mode squeezed light in the continuous variable EPR-state are considered. They are based on the integrals of motion, which allow conserving quantum correlations whereas the power of each mode may increase. One of these schemes involves a three-photon parametric process in a nonlinear transparent medium and second is a Raman type interaction of light with atomic ensemble.Comment: 3 pages, revtex4, no figure