Special issue on basics and applications in quantum optics

Quantum technologies are advancing very rapidly and have the potential to innovate communication and computing far beyond current possibilities. Among the possible plat- forms suitable to run quantum technology protocols, in the last decades quantum optics has received a lot of attention for the handiness and versatility of optical systems. In addition to studying the fundamentals of quantum mechanics, quantum optical states have been exploited for several applications, such as quantum-state engineering, quantum communication and quantum cryptography protocols, enhanced metrology and sensing, quantum optical integrated circuits, quantum imaging, and quantum biological effects. In this Special Issue, we collect some papers and also a review on some recent research activities that show the potential of quantum optics for the advancement of quantum technologies

Reliable source of conditional non-Gaussian states from single-mode thermal fields

We address both theoretically and experimentally the generation of pulsed non-Gaussian states from classical Gaussian ones by means of conditional measurements. The setup relies on a beam splitter and a pair of linear photodetectors able to resolve up to tens of photons in the two outputs. We show the reliability of the setup and the good agreement with the theory for a single-mode thermal field entering the beam splitter and present a thorough characterization of the photon statistics of the conditional states.Comment: 18 pages, 12 figure

Generalized Nash Equilibrium and Market Coupling in the European Power System

Market Coupling'' is currently seen as the most advanced market design in the restructuring of the European electricity market. Market coupling, by construction, introduces what is generally referred to as an incomplete market: it leaves several constraints out of the market and hence avoids pricing them. This may or may not have important consequences in practice depending on the case on hand. QuasiVariational Inequality problems. We apply one of these methods to a subproblem of market coupling namely the coordination of counter-trading. This problem is an illustration of a more general question encountered for instance in hierarchical planning in production management. We first discuss the economic interpretation of the Quasi-Variational Inequality problem. We then apply the algorithmic approach to a set of stylized case studies in order to illustrate the impact of different organizations of counter-trading. The paper emphazises the structuring of the problem. A companion paper considers the full problem of market coupling and counter-trading and presents a more extensive numerical analysis

Conditional measurements on multimode pairwise entangled states from spontaneous parametric downconversion

We address the intrinsic multimode nature of the quantum state of light obtained by pulsed spontaneous parametric downconversion and develop a theoretical model based only on experimentally accessible quantities. We exploit the pairwise entanglement as a resource for conditional multimode measurements and derive closed formulas for the detection probability and the density matrix of the conditional states. We present a set of experiments performed to validate our model in different conditions that are in excellent agreement with experimental data. Finally, we evaluate nonGaussianity of the conditional states obtained from our source with the aim of discussing the effects of the different experimental parameters on the efficacy of this type of conditional state preparation

State reconstruction by on/off measurements

We demonstrate a state reconstruction technique which provides either the Wigner function or the density matrix of a field mode and requires only avalanche photodetectors, without any phase or amplitude discrimination power. It represents an alternative, of simpler implementation, to quantum homodyne tomography.Comment: 6 pages, 4 figures, revised and enlarged versio

Gauss-Seidel method for multi-valued inclusions with Z mappings

We consider a problem of solution of a multi-valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss-Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under rather mild additional assumptions. Some results of numerical experiments are also presented. © 2011 Springer Science+Business Media, LLC

Gauss-Seidel method for multi-valued inclusions with Z mappings

We consider a problem of solution of a multi-valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss-Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under rather mild additional assumptions. Some results of numerical experiments are also presented. © 2011 Springer Science+Business Media, LLC

Noncooperative games with vector payoffs under relative pseudomonotonicity

We consider the Nash equilibrium problem with vector payoffs in a topological vector space. By employing the recent concept of relative (pseudo) monotonicity, we establish several existence results for vector Nash equilibria and vector equilibria. The results strengthen in a major way existence results for vector equilibrium problems which were based on the usual (generalized) monotonicity concepts

Characterizations of relatively generalized monotone maps

New concepts of relative monotonicity were introduced in Konnov (Oper Res Lett 28:21-26, 2001a) which extend the usual ones. These concepts enable us to establish new existence and uniqueness results for variational inequality problems over product sets. This paper presents first-order characterizations of new (generalized) monotonicity concepts. Specialized results are obtained for the affine case. © Springer-Verlag 2007

Geometry of perturbed Gaussian states and quantum estimation

We address the nonGaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that nG of the perturbed state may be written as the quantum Fisher information (QFI) distance minus a term depending on the infinitesimal energy change, i.e. it provides a lower bound to statistical distinguishability. Upon moving on isoenergetic surfaces in a neighbourhood of a Gaussian state, nG thus coincides with a proper distance in the Hilbert space and exactly quantifies the statistical distinguishability of the perturbations. On the other hand, for perturbations leaving the covariance matrix unperturbed we show that nG provides an upper bound to the QFI. Our results show that the geometry of nonGaussian states in the neighbourhood of a Gaussian state is definitely not trivial and cannot be subsumed by a differential structure. Nevertheless, the analysis of perturbations to a Gaussian state reveals that nG may be a resource for quantum estimation. The nG of specific families of perturbed Gaussian states is analyzed in some details with the aim of finding the maximally non Gaussian state obtainable from a given Gaussian one.Comment: 7 pages, 1 figure, revised versio