A derivation of two transformation formulas contiguous to that of Kummer’s second theorem via a differential equation approach

The purpose of this note is to provide an alternative proof of two transformation formulas contiguous to that of Kummer’s second transformation for the confluent hypergeometric function 1F1 using a differential equation approach

A note on a hypergeometric transformation formula due to Slater with an application

In this note we state (with minor corrections) and give an alternative proof of a very general hypergeometric transformation formula due to Slater. As an application, we obtain a new hypergeometric transformation formula for a 5F4(−1) series with one pair of parameters differing by unity expressed as a linear combination of two 3F2(1) series

The role of initial entanglement and nonGaussianity in the decoherence of photon number entangled states evolving in a noisy channel

We address the degradation of continuous variable (CV) entanglement in a noisy channel focusing on the set of photon-number entangled states. We exploit several separability criteria and compare the resulting separation times with the value of non-Gaussianity at any time, thus showing that in the low-temperature regime: i) non-Gaussianity is a bound for the relative entropy of entanglement and ii) Simon' criterion provides a reliable estimate of the separation time also for nonGaussian states. We provide several evidences supporting the conjecture that Gaussian entanglement is the most robust against noise, i.e. it survives longer than nonGaussian one, and that this may be a general feature for CV systems in Markovian channels.Comment: revised version, title and figures change

Comments on "New hypergeometric identities arising from Gauss’s second summation theorem"

In 1997, Exton [J. Comput. Appl. Math. 88 (1997) 269–274] obtained a general transfor- mation involving hypergeometric functions by elementary manipulation of series. A number of hypergeometric identities not previously recorded in the literature were then deduced by application of Gauss’ second summation theorem and other known hypergeometric summa- tion theorems. However, many of the results stated by Exton contain errors. It is the purpose of this note to present the corrected forms of these hypergeometric identities

Remote state preparation and teleportation in phase space

Continuous variable remote state preparation and teleportation are analyzed using Wigner functions in phase space. We suggest a remote squeezed state preparation scheme between two parties sharing an entangled twin beam, where homodyne detection on one beam is used as a conditional source of squeezing for the other beam. The scheme works also with noisy measurements, and provide squeezing if the homodyne quantum efficiency is larger than 50%. Phase space approach is shown to provide a convenient framework to describe teleportation as a generalized conditional measurement, and to evaluate relevant degrading effects, such the finite amount of entanglement, the losses along the line, and the nonunit quantum efficiency at the sender location.Comment: 2 figures, revised version to appear in J.Opt.

Optimized quantum nondemolition measurement of a field quadrature

We suggest an interferometric scheme assisted by squeezing and linear feedback to realize the whole class of field-quadrature quantum nondemolition measurements, from Von Neumann projective measurement to fully non-destructive non-informative one. In our setup, the signal under investigation is mixed with a squeezed probe in an interferometer and, at the output, one of the two modes is revealed through homodyne detection. The second beam is then amplitude-modulated according to the outcome of the measurement, and finally squeezed according to the transmittivity of the interferometer. Using strongly squeezed or anti-squeezed probes respectively, one achieves either a projective measurement, i.e. homodyne statistics arbitrarily close to the intrinsic quadrature distribution of the signal, and conditional outputs approaching the corresponding eigenstates, or fully non-destructive one, characterized by an almost uniform homodyne statistics, and by an output state arbitrarily close to the input signal. By varying the squeezing between these two extremes, or simply by tuning the internal phase-shift of the interferometer, the whole set of intermediate cases can also be obtained. In particular, an optimal quantum nondemolition measurement of quadrature can be achieved, which minimizes the information gain versus state disturbance trade-off