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We study two-spin entanglement and order parameter fluctuations as a function of the system size in the XY model in a transverse field and in the isotropic XXX model. Both models are characterized by the occurrence of ground state degeneracy also when systems of finite size are considered. This is always true for the XXX model, but only at the factorizing field for the XY model. We study the size dependence of symmetric states, which, in the presence of degeneracy, can be expanded as a linear combination of broken symmetry states. We show that, while the XY model looses its quantum superposition content exponentially with the size $N$, a decrease of the order of 1/N is observed when the XXX model is considered. The emergence of two qualitatively different regimes is directly related to the difference in the symmetry of the models.

A system of two interacting photon modes, without constraints on the photon number, in the presence of a Kerr nonlinearity, exhibits BEC if the transfer amplitude is greater than the mode frequency. A symmetry-breaking field (SBF) can be introduced by taking into account a classical electron current. The ground state, in the limit of small nonlinearity, becomes a squeezed state, and thus the modes become entangled. The smaller is the SBF, the greater is entanglement. Superfluid-like behavior is observed in the study of entanglement growth from an initial coherent state, since in the short-time range the growth does not depend on the SBF amplitude, and on the initial state amplitude. On the other hand, the latter is the only parameter which determines entanglement in the absence of the SBF.

A diffusion process is usually assumed for the phase of the order parameter of a Bose system of finite size. The theoretical basis is limited to the so called Bogoliubov approximation. We show that a suitable generalization of the Hartree-Fock-Bogoliubov approach recovers phase diffusion.

We present a model where two magnetic impurities in a discrete tight-binding ring become entangled because of scattering processes associated to the injection of a conduction electron. We introduce a weak coupling approximation that allows us to solve the problem in a analytical way and compare the theory with the exact numerical results. We obtain the generation of entanglement both in a deterministic way and in a probabilistic one. The first case is intrinsically related to the structure of the two-impurity reduced density matrix, while the second one occurs when a projection on the electron state is performed.

We present a model to realize a probabilistic conditional sign flip gate using only linear optics. The gate operates in the space of number state qubits and is obtained by a nonconventional use of the teleportation protocol. Both a destructive and a nondestructive version of the gate are presented. In the former case an Hadamard gate on the control qubit is combined with a projective teleportation scheme mixing control and target. The success probability is 1/2. In the latter case we need a quantum encoder realized via the interaction of the control qubit with an ancillary state composed of two maximally entangled photons. The success probability is 1/4.