We address the generation of fully inseparable three-mode entangled states of radiation by interlinked nonlinear interactions in ${\chi }^{(2)}$ media. We show how three-mode entanglement can be used to realize symmetric and asymmetric telecloning machines, which achieve optimal fidelity for coherent states. An experimental implementation involving a single nonlinear crystal in which the two interactions take place simultaneously is suggested. Preliminary experimental results showing the feasibility and the effectiveness of the interaction scheme with a seeded crystal are also presented.

We implement a direct detection scheme based on hybrid photodetectors to experimentally investigate high-order correlations for detected photons by means of experimentally accessible quantities. The scheme is self-consistent, allowing the estimation of all the involved parameters (quantum efficiency, number of modes, and average energy). In particular, we show how high-order correlation functions can be exploited to fully characterize bipartite multimode states in regimes realistic for quantum technology, that is, in the mesoscopic photon-number domain and with limited quantum efficiency. Furthermore, we introduce a nonclassicality criterion based on a simple linear combination of high-order correlation functions.

Twin-beam coherence properties are analyzed in both spatial and spectral domains at high gain, including also the regime of pump depletion. We show an increase in the size of the intensity autocorrelation and cross-correlation areas at increasing pump power, replaced by a decrease in the pump depletion regime. This effect is interpreted as a progressive loss in the mode selection occurring at high-gain amplification. The experimental determination of the number of spatiospectral modes from the measurements of the $g^{\left(2\right)}$-intensity autocorrelation coefficient confirms this explanation.

We demonstrate the effect of multiple-photon subtraction on the generation of conditional states in the pulsed regime. Our experimental scheme relies on a beam splitter (BS) and a pair of linear photodetectors that are able to resolve up to tens of photons. We use a single-mode thermal field at the input port of the BS to test the reliability of our scheme, and we show good agreement with the theory by fully characterizing the conditional outgoing states in terms of photon-number statistics and non-Gaussianity.

We present a compact experimental realization of the interaction among five field modes in a ${\chi }^{\left(2\right)}$ nonlinear crystal. The classical evolution of the fields can be analytically described assuming that two of the fields play the role of nondepleted pumps. A peculiar behavior appears that has been experimentally verified. If one of the fields has a nonzero input amplitude, then the other two fields at the output are holographic replicas of the input signal.