We study the information transmission through a quantum channel, defined over a continuous alphabet and losing its energy en route, in presence of correlated noise among different channel uses. We then show that entangled inputs improve the rate of transmission of such a channel.

We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function σ(η) of the conformal time η, called the auxiliary field equation. At the classical level, σ(η) can be expressed by means of two independent solutions of the "master equation" to which the perturbed Einstein equations for the gravitational waves can be reduced.At the quantum level, all the significant physical quantities can be formulated using Bogolubov transformations and the operator quadratic Hamiltonian corresponding to the classical version of a damped parametrically excited oscillator where the varying mass is replaced by the square cosmological scale factor a 2 (η). A quantum approach to the generation of gravitational waves is proposed on the grounds of the previous η−dependent Hamiltonian. An estimate in terms of σ(η) and a(η) of the destruction of quantum coherence due to the gravitational evolution and an exact expression for the phase of a gravitational wave corresponding to any value of η are also obtained. We conclude by discussing a few applications to quasi-de Sitter and standard de Sitter scenarios.

Time-dependent dynamical systems with a particular emphasis on models attaining the minimum value of uncertainty formula are considered. The role of the Bogolubov coefficients, in general and in the context of the loss of minimum uncertainty, is analyzed. Different fluctuation values on squeezed states are performed. The decoherence energy is parametrized by an angle ϕ and turns out to vanish whenever ϕ=π. An application to the Paul trap theory is discussed.

We study the security of the information transmission between two honest parties realized through a lossy bosonic memory channel when losses are captured by a dishonest party. We then show that entangled inputs can enhance the private information of such a channel, which however does never overcome that of unentangled inputs in absence of memory.

Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with in¯nite dimensional Hilbert space. To this aim, we consider the completely solvable Moshinsky's model of two linearly coupled harmonic oscillators. Also, for small values of the couplings, the entanglement of the ground state is nonlinearly related to the correlation energy, involving logarithmic or algebraic corrections. Then, looking for witness observables of the entanglement, we show how to give a physical interpretation of the correlation energy. In particular, we have proven that there exists a set of separable states, continuously connected with the HartreeÀFock state, which may have a larger overlap with the exact ground state, but also a larger energy expectation value. In this sense, the correlation energy provides an entanglement gap, i.e. an energy scale, under which measurements performed on the 1-particle harmonic sub-system can discriminate the ground state from any other separated state of the system. However, in order to verify the generality of the procedure, we have compared the energy distribution cumulants for the 1-particle harmonic sub-system of the Moshinsky's model with the case of a coupling with a damping Ohmic bath at 0 temperature.