The optimal discrimination of two Gaussian channels is a central problem in quantum information theory. In this talk we discuss how the use of quantum entanglement can reduce the error probability which affects this statistical problem, giving a dramatic advantage over the use of classical light in the regime of few photons.
This enhancement is exploited in two non-trivial tasks: the detection of low-reflectivity targets (quantum illumination [1,2]) and the readout of digital memories (quantum reading ).
We study ordinary solitons and gap solitons (GSs) in the framework of the one-dimensional Gross-Pitaevskii equation (GPE) with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of (in)commensurability between the lattices, development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons.