## A Case of Entanglement Generation Between Causally Disconnected Atoms.

We analyze the entanglement generated in a finite time between a pair of space-like separated atoms, one of which emits a photon. As we show to order e^2, the origin of entanglement can be traced back to the uncertainty about which one of the atoms emitted the photon. We check this by comparing the time behaviors of the emission processes allowed by energy conservation vs. those forbidden by the same reason. No physical signal propagates between the atoms in the processes considered, however an effective light cone separating non-entangled from entangled regions in space-time emerges from our calculations.

## Atom-Atom Entanglement Generated at Early Times by Two Photon Emission.

We analyze entanglement generation between a pair of neutral two-level atoms that are initially excited in a common electromagnetic vacuum. The nonlocal correlations that appear due to the interaction with the field can become entanglement when the field state is known. We distinguish two different situations: in the first, the field remains in the vacuum state and in the second, two photons are present in the final state. In both cases, we study the dependence of the entanglement on time and interatomic distance, at ranges related with locality issues.

## Correlated Hopping of Bosonic Atoms Induced by Optical Lattices.

In this work, we analyze a particular setup with ultracold atoms trapped in state-dependent lattices. We show that any asymmetry in the contact interaction translates into one of two classes of correlated hopping. After deriving the effective lattice Hamiltonian for the atoms, we obtain analytically and numerically the different phases and quantum phase transitions. We find for weak correlated hopping both Mott insulators and charge density waves, while for stronger correlated hopping the system transitions into a pair superfluid. We demonstrate that this phase exists for a wide range of interaction asymmetries and has interesting correlation properties that differentiate it from an ordinary atomic Bose–Einstein condensate.

## Dissipation-Induced Hard-Core Boson Gas in an Optical Lattice.

We present a theoretical investigation of a lattice Tonks–Girardeau gas that is created by inelastic, instead of elastic interactions. An analytical calculation shows that in the limit of strong two-body losses, the dynamics of the system is effectively that of a hard-core boson gas. We also derive an analytic expression for the effective loss rate. We find good agreement between these analytical results and results from a rigorous numerical calculation. The hard-core character of the particles is visible both in a reduced effective loss rate and in the momentum distribution of the gas.

## Fermionic Entanglement that Survives a Black Hole.

We introduce an arbitrary number of accessible modes when analyzing bipartite entanglement degradation due to Unruh effect between two partners Alice and Rob. Under the single mode approximation (SMA) a fermion field only had a few accessible levels due to Pauli exclusion principle, conversely to bosonic fields which had an infinite number of excitable levels. This was argued to justify entanglement survival in the fermionic case in the SMA infinite acceleration limit. Here we relax SMA. Hence, an infinite number of modes are excited as the observer Rob accelerates, even for a fermion field. We will prove that, despite this analogy with the bosonic case, entanglement loss is limited. We will show that this comes from fermionic statistics through the characteristic structure it imposes on the infinite dimensional density matrix for Rob. Surprisingly, the surviving entanglement is independent of the specific maximally entangled state chosen, the kind of fermionic field analyzed, and the number of accessible modes considered. We shall discuss whether this surviving entanglement goes beyond the purely statistical correlations, giving insight concerning the black hole information paradox.

## Generation of Atom-Atom Correlations Inside and Outside the Mutual Light Cone.

We analyze whether a pair of neutral two level atoms can become entangled in a finite time while they remain causally disconnected. The interaction with the e. m. field is treated perturbatively in the electric dipole approximation. We start from an initial vacuum state and obtain the final atomic correlations for the cases where n = 0, 1, or 2 photons are produced in a time t, and also when the final field state is unknown. Our results show that correlations are sizable inside and outside the mutual light cone for n= 1 and 2, and also that quantum correlations become classical by tracing over the field state. For n = 0 we obtain entanglement generation by photon propagation between the atoms, the correlations come from the indistinguishability of the source for n = 1, and may give rise to entanglement swapping for n = 2.

## Lieb-Liniger Model of a Dissipation-Induced Tonks-Girardeau Gas.

We consider soft-photon effects (ir structure of QED) on the construction of physical qubits. Soft photons appear when we build charged qubits from the asymptotic states of QED. This construction is necessary in order to include the effect of soft photons on entanglement measures. The nonexistence of free charged particles (due to the long range of QED interactions) leads us to question the sense of the very concept of free charged qubit. In this work, using the “dressing” formalism, we build physical charged qubits from dressed fields which have the correct asymptotic behavior, are gauge invariant, have propagators with a particle pole structure, and are free from infrared divergences. Finally, we discuss the impact of the soft corrections on the entanglement measures.

## Microwave Photon Detector in Circuit QED.

Quantum optical photodetection has occupied a central role in understanding radiation-matter interactions. It has also contributed to the development of atomic physics and quantum optics, including applications to metrology, spectroscopy, and quantum information processing. The quantum microwave regime, originally explored using cavities and atoms, is seeing a novel boost with the generation of nonclassical propagating fields in circuit quantum electrodynamics (QED). This promising field, involving potential developments in quantum information with microwave photons, suffers from the absence of photodetectors. In this Letter we design a metamaterial composed of discrete superconducting elements that implements a high-efficiency microwave photon detector. Our design consists of a microwave guide coupled to an array of metastable quantum circuits, whose internal states are irreversibly changed due to the absorption of photons. This proposal can be widely applied to different physical systems and can be generalized to implement a microwave photon counter.

## Operational Determination of Multiqubit Entanglement Classes via Tuning of Local Operations.

We present a physical setup with which it is possible to produce arbitrary symmetric long-lived multiqubit entangled states in the internal ground levels of photon emitters, including the paradigmatic Greenberger-Horne-Zeilinger and W states. In the case of three emitters, where each tripartite entangled state belongs to one of two well-defined entanglement classes, we prove a one-to-one correspondence between well-defined sets of experimental parameters, i.e., locally tunable polarizer orientations, and multiqubit entanglement classes inside the symmetric subspace.

## Photodetection of Propagating Quantum Microwaves in Circuit QED.

We develop the theory of a metamaterial composed of an array of discrete quantum absorbers inside a one-dimensional waveguide that implements a high-efficiency microwave photon detector. A basic design consists of a few metastable superconducting nanocircuits spread inside and coupled to a one-dimensional waveguide in a circuit QED setup. The arrival of a {\\it propagating} quantum microwave field induces an irreversible change in the population of the internal levels of the absorbers, due to a selective absorption of photon excitations. This design is studied using a formal but simple quantum field theory, which allows us to evaluate the single-photon absorption efficiency for one and many absorber setups. As an example, we consider a particular design that combines a coplanar coaxial waveguide with superconducting phase qubits, a natural but not exclusive playground for experimental implementations. This work and a possible experimental realization may stimulate the possible arrival of 'all-optical' quantum information processing with propagating quantum microwaves, where a microwave photodetector could play a key role.

## Photon Exchange and Correlation Transfer in Atom-Atom Entanglement Dynamics.

We analyze the entanglement dynamics of a system composed by a pair of neutral two-level atoms that are initially entangled, and the electromagnetic field, initially in the vacuum state, within the formalism of perturbative quantum field theory up to the second order. We show that entanglement sudden death and revival can occur while the atoms remain spacelike-separated and therefore cannot be related with photon exchange between the atoms. We interpret these phenomena as the consequence of a transfer of atom-atom entanglement to atom-field entanglement and viceversa. We also consider the different bi-partitions of the system, finding similar relationships between their entanglement evolutions.

## Physical Qubits from Charged Particles: Infrared Divergences in Quantum Information.

We consider soft-photon effects (ir structure of QED) on the construction of physical qubits. Soft photons appear when we build charged qubits from the asymptotic states of QED. This construction is necessary in order to include the effect of soft photons on entanglement measures. The nonexistence of free charged particles (due to the long range of QED interactions) leads us to question the sense of the very concept of free charged qubit. In this work, using the “dressing” formalism, we build physical charged qubits from dressed fields which have the correct asymptotic behavior, are gauge invariant, have propagators with a particle pole structure, and are free from infrared divergences. Finally, we discuss the impact of the soft corrections on the entanglement measures.

## Preparation of Decoherence-Free Cluster States with Optical Superlattices.

We present a protocol to prepare decoherence free cluster states using ultracold atoms loaded in a two dimensional superlattice. The superlattice geometry leads to an array of 2x2 plaquettes, each of them holding four spin-1/2 particles that can be used for encoding a single logical qubit in the two-fold singlet subspace, insensitive to uniform magnetic field fluctuations in any direction. Dynamical manipulation of the supperlattice yields distinct inter and intra plaquette interactions and permits to realize one qubit and two qubit gates with high fidelity, leading to the generation of universal cluster states for measurement based quantum computation. Our proposal based on inter and intra plaquette interactions also opens the path to study polymerized Hamiltonians which support ground states describing arbitrary quantum circuits.

## Spin and Occupation Number Entanglement of Dirac Fields for Non-Inertial Observers.

We investigate the Unruh effect on entanglement taking into account the spin degree of freedom of the Dirac field. We analyze spin Bell states in this setting, obtaining their entanglement dependance on the acceleration of one of the partners. Then, we consider simple analogs to the occupation number entangled state |00>+|11>, but with spin quantum numbers for |11> showing that, despite their apparent similitude, while the spinless case is always qubit x qubit, for the spin case acceleration produces a qubit x qu4it state. We also introduce a procedure to consistently erase the spin information from our setting preserving occupation numbers. We show how the maximally entangled state for occupation number emerges from our setting, we also analyze its entanglement dependance on acceleration, obtaining a greater entanglement degradation than in the spinless case.