## Vacuum representation and the Reeh-Schlieder theorem

Fernando LLedó (UAM)

In this lecture we introduce the notion of the vacuum representation and show, under certain assumptions, its uniqueness. We will also give in this mathematical frame a complete proof of the Reeh-Schlieder theorem.

Seminar Room, Serrano 121 (CFMAC)

## Topological Quantum Computation: an Introduction

Miguel Ángel Martín-Delgado (UCM)

We introduce the basic notions describing topological quantum error correction codes and its extension to quantum computation. The underlying physical systems are strongly correlated systems of particles showing a topological order. These orders can be described by quantum Hamiltonians defined on lattices such that the degeneration of the ground state depends on the lattice topology. These codes gives rise to topological orders with very interesting features.

Seminar Room, Serrano 121 (CFMAC)

## Haag-Kastler axioms and first consequences

Fernando LLedó (UAM)

Haag´s approach to quantum field theory puts the notion of locality in the middle of the synthesis of quantum mechanics and special relativity. Non-local aspects in quantum theory appear in connection with states. In this lecture we formulate the axioms of quantum field theory in the context defined by a family of von Neumann algebras localized in open and bounded regions of Minkowski space. We will also mention some consequences of these axioms.

Seminar Room, Serrano 121 (CFMAC)

## Quantum circuits

Juan José García Ripoll (IFF-CSIC)

In this talk we will introduce quantum circuit theory. We will see how the diverse elements at hand – cables, inductances, capacitors, Josephson junctions – can be used for quantum information processing i. e. to create qubits, artificial atoms, non classical microwave states, cavities, etc. Along with the theory, we will revise the main experiments in this field, which developed in the last four years. We will also review the main challenges and obstacles to progress.

Seminar Room, Serrano 121 (CFMAC)

## Operator algebras as a natural language for quantum theory

Fernando LLedó (UAM)

In this first lecture we will introduce informally the language of operator algebras, in particular, C*- and von Neumann algebras. These classes of operator algebras and their family of states will be used later in order to formulate the axioms of quantum field theory. We will also mention some historical contributions of these algebras to the development of quantum mechanics and present some examples relevant to quantum theory.

Seminar Room, Serrano 121 (CFMAC)

## Vacuum correlations and photon propagation in spatially separated entangled systems

Juan León (IFF-CSIC)

In this talk we will obtain perturbatively the correlations predicted by quantum theory for a system of two atoms which remain spatially separated. The striking phenomena of entanglement death and rebirth will be traced back to the reshuffling of these correlations among the atoms and the e.m. field. Apparent causality violations will appear as an artifact coming from the non-local specification imposed on the states.

Seminar Room, Serrano 121 (CFMAC)