Abstract:
In recent years quantum statistical mechanics have benefited of cultural interchanges with quantum information science. There is a bulk of evidence that quantifying the entanglement allows a fine analysis of many relevant properties of many-body quantum systems. Here we review the relation between entanglement and the various type of magnetic order occurring in interacting spin systems.

Abstract:
Information capacities achievable in the multi-parallel-use scenarios are employed to characterize the quantum correlations in unmodulated spin chains. By studying the qubit amplitude damping channel, we calculate the quantum capacity $Q$, the entanglement assisted capacity $C_E$, and the classical capacity $C_1$ of a spin chain with ferromagnetic Heisenberg interactions.

Abstract:
By means of analytical and numerical methods we analyze the phase diagram of polaritons in one-dimensional coupled cavities. We locate the phase boundary, discuss the behavior of the polariton compressibility and visibility fringes across the critical point, and find a non-trivial scaling of the phase boundary as a function of the number of atoms inside each cavity. We also predict the emergence of a polaritonic glassy phase when the number of atoms fluctuates from cavity to cavity.

Abstract:
Coupled quantum electrodynamics (QED) cavities have been recently proposed as new systems to simulate a variety of equilibrium and non-equilibrium many-body phenomena. We present a brief review of their main properties together with a survey of the last developments of the field and some perspectives concerning their experimental realizations and possible new theoretical directions.

Abstract:
We study the critical behavior of the conductivity $\sigma(\omega)$ at the zero temperature superconductor-Mott insulator transition in $d$ space-time dimensions for a model of bosons with short-range interaction and no disorder. We obtain $\sigma(\omega_n ) = (4e^2/\hbar) \sigma_{\epsilon} \omega_n^{1-\epsilon}$, as predicted by the scaling theory, and the prefactor $\sigma_{\epsilon}$ is calculated in the $\epsilon$-expansion, to order $\epsilon ^2$ ($\epsilon = 4-d$). In two spatial dimensions, ($d=3$), we find a value of the universal conductance $\sigma^\star =0.315 (4e^2/h)$, in good agreement with the known Monte Carlo results.

Abstract:
By means of the Density Matrix Renormalization Group technique, we accurately determine the zero-temperature phase diagram of the one-dimensional extended Bose Hubbard model with on-site and nearest-neighbor interactions. We analyze the scaling of the charge and of the neutral ground-state energy gaps, as well as of various order parameters. In this way we come to an accurate location of the boundaries between the superfluid and the insulating phases. In this last region we are able to distinguish between the conventional Mott insulating and density-wave phases, and the Haldane Insulator phase displaying long-range string ordering, as originally predicted by E.G. Dalla Torre, E. Berg and E. Altman in Phys. Rev. Lett. 97, 260401 (2006).

Abstract:
We analyze possible implementations of quantum algorithms in a system of (macroscopic) Josephson charge qubits. System layout and parameters to realize the Deutsch algorithm with up to three qubits are provided. Special attention is paid to the necessity of entangled states in the various implementations. Further, we demonstrate explicitely that the gates to implement the Bernstein-Vazirani algorithm can be realized by using a system of uncoupled qubits.

Abstract:
In this Letter we study thermoelectric effects in ultra small quantum dots. We study the behaviour of the thermopower, Peltier coefficient and thermal conductance both in the sequencial tunneling regime and in the regime where Kondo correlations develope. Both cases of linear response and non-equilibrium induced by strong temperature gradients are considered. The thermopower is a very sensitive tool to detect Kondo correlations. It changes sign both as a function of temperature and temperature gradient. We also discuss violations of the Wiedemann-Franz law.

Abstract:
We study resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We obtain a formula for the Andreev current and apply it to discuss the linear and non-linear transport in the nonperturbative regime, where the effects of the Kondo resonance on the two particle tunneling arise. In particular we notice an enhancement of the Kondo anomaly in the $I-V$ characteristics due to the superconducting electrode.

Abstract:
The counting statistics (CS) for charges passing through a coherent conductor is the most general quantity that characterizes electronic transport. CS not only depends on the transport properties of the conductor but also depends on the correlations among particles which compose the incident beam. In this paper we present general results for the CS of entangled electron pairs traversing a beam splitter and we show that the probability that Q charges have passed is not binomial, as in the uncorrelated case, but rather it is symmetric with respect to the average transferred charge. We furthermore consider the joint probability for transmitted charges of a given spin and we show that the signature of entanglement distinctly appears in a correlation which is not present for the non-entangled case.