We study the exact entanglement dynamics of two atoms in a lossy resonator. Besides discussing the steady-state entanglement, we show that in the strong coupling regime the system-reservoir correlations induce entanglement revivals and oscillations and propose a strategy to fight against the deterioration of the entanglement using the quantum Zeno effect.

We introduce a tool for the quantitative characterization of the departure from Markovianity of a given dynamical process. Our tool can be applied to a generic N-level system and extended straightforwardly to Gaussian continuous-variable systems. It is linked to the change of the volume of physical states that are dynamically accessible to a system and provides qualitative expectations in agreement with some of the analogous tools proposed so far. We illustrate its predictive power by tackling a few canonical examples

We study the dynamics of quantum correlations in a class of exactly solvable Ising-type models. We analyze in particular the time evolution of initial Bell states created in a fully polarized background and on the ground state. We find that the pairwise entanglement propagates with a velocity proportional to the reduced interaction for all the four Bell states. Singlet-like states are favored during the propagation, in the sense that triplet-like states change their character during the propagation under certain circumstances. Characteristic for the anisotropic models is the instantaneous creation of pairwise entanglement from a fully polarized state; furthermore, the propagation of pairwise entanglement is suppressed in favor of a creation of different types of entanglement. The "entanglement wave" evolving from a Bell state on the ground state turns out to be very localized in space-time. Further support to a recently formulated conjecture on entanglement sharing is given.

We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we show that a specific fluctuation relation for the entropy production associated with the inner friction exists, which allows the inner friction to be written in terms of its cumulants.PACS numbers: 05.70. Ln, With the increasing ability to manufacture and control microscopic systems, we are approaching the limit where quantum fluctuations, as well as thermal ones, become important when trying to put nanomachines and quantum engines to useful purposes [1, 2]. To discuss engines performances, e.g. for heat-to-work conversion, one typically starts by considering reversible transformations that drive the system from an equilibrium configuration to another one. However, if the system is pushed faster than the thermalization time, such transformations are irreversible, and can lead outside the manifold of equilibrium states [3][4][5]. Nonetheless, these processes are of interest as the reversible protocols, despite enjoying very good efficiencies, give rise to very small output powers [6]. The irreversibility of a process is hence related both to better performances and to lack of control, leading to entropy production [7].To analyze irreversibility and entropy production in the quantum realm, we consider a system initially kept in equilibrium and subject to a finite time adiabatic transformation. While its initial state is prepared by keeping it in contact with a thermal bath, the system is then thermally isolated and subject to a parametric change of its Hamiltonian from an initial H i = H[λ i ] to a final H f = H[λ f ] in a finite time τ . The process is defined by the time variation of the work parameter λ(t), changing from λ(t = 0) = λ i to λ(τ ) = λ f .The work w performed on the system during such a process is a stochastic variable with an associated probability density p(w) [4,8,9], which can be reconstructed experimentally [10,11]

A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Loschmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore non-Markovianity is an indicator of criticality in the model considered here.

Exploiting the relative entropy of coherence, we isolate the coherent contribution in the energetics of a driven non-equilibrium quantum system. We prove that a division of the irreversible work can be made into a coherent and incoherent part, which provides an operational criterion for quantifying the coherent contribution in a generic non-equilibrium transformation on a closed quantum system. We then study such a contribution in two physical models of a driven qubit and kicked rotor. In addition, we also show that coherence generation is connected to the non-adiabaticity of a processes, for which it gives the dominant contribution for slow-enough transformation. The amount of generated coherence in the energy eigenbasis is equivalent to the change in diagonal entropy, and here we show that it fulfills a fluctuation theorem.

We discuss the emergence of spontaneous synchronization for an open spin-pair system interacting only via a common environment. Under suitable conditions, and even in the presence of detuning between the natural precession frequencies of the two spins, they are shown to reach a long-lasting transient behavior where they oscillate in phase. We explore the connection between the emergence of such a behavior and the establishment of robust quantum correlations between the two spins, analyzing differences between dissipative and dephasing effects. In particular, in the regime in which synchronization occurs, quantum correlations are more robust for shorter synchronization times and this is related to a separation between system decay rates.

We propose a scheme to implement a quantum information transfer protocol with a superconducting circuit and Josephson charge qubits. The information exchange is mediated by an L-C resonator used as a data bus. The main decoherence sources are analyzed in detail. PACS numbers: 74.50.+r,03.67.Hk,73.23.Hk One of the main purposes of quantum information processing is the faithful transmission of quantum states between distant parties, eventually exploiting entanglement among subsystems. Examples include quantum teleportation 1 and dense coding 2 , both of them demonstrated using entangled photon pairs 3 , with the ultimate aim of performing quantum cryptography 4 . Until now, however, much of the work has been done within the realm of quantum optics 5 and very little efforts have been devoted to describe and implement these phenomena with solid state devices. On the other hand, nano-electronic devices have been proposed as candidates for quantum computer implementation 6,7,8,9 since they are easily embedded in electronic circuits and scaled up to contain a large number of qubits. In particular, superconducting Josephson junction circuits, whose fabrication is now performed with well established lithographyc methods, combine the intrinsic stability of the superconducting phase with the possibility of controlling the circuit dynamics through manipulations of the applied voltages or magnetic fluxes 10 . Direct experimental evidence that a single-Cooper-pair box can be used as a controllable coherent two level system has been provided by Nakamura et al 11 . Either the charge on the island or the phase differences at junction can be used to store and manipulate quantum information 12 , the two regimes being characterized by dominating charging and Josephson energies, respectively. Here, we concentrate on the charge regime and propose a set-up that allows quantum information transfer and entanglement generation between two Josephson qubits. The circuit is designed so that interaction between the two subsystems is mediated by an L-C resonator, see Fig. 1, playing the role of a data bus. The spirit of the proposal is very similar to the Cirac-Zoller scheme for trapped ion qubit 13 . As will be shown below, this set-up is flexible enough to allow for quantum information transfer from one qubit to another and for the generation of Bell states. Furthermore, the circuit can be generalized to include more qubits and we give the necessary prescriptions to implement a universal set of quantum gates.The coupling of a single charge qubit to a large Josephson junction (which may implement the resonator) has been recently exploited to perform on chip quantum state measurements 15 , and to prepare a mesoscopic Schrödinger cat state 16 . We consider here a similar coupling, but replace the single junction with a SQUID to achieve a tuning of the Josephson energy 7 , which allows to operate in both the dispersive and the resonant coupling regimes, as required by the protocols described below.We first analyze the model for a single qubi...