Entanglement is the main quantum property that makes quantum information protocols more powerful than any classical counterpart. Moreover, understanding entanglement allows a better comprehension of physical phenomena in the fields of condensed matter, statistical physics, and quantum optics among others. The open questions on entanglement range from fundamental to practical issues. How to characterize the entanglement of quantum systems? What is entanglement useful for? What is the relation between entanglement and other physical phenomena? These are some open questions we are faced with nowadays.

This thesis contains some original results in this field. Some of the addressed questions rely on the mathematical description of entanglement while others on its description in some physical systems. More specifically,

(i) it will be shown a relation between two quantifiers of entanglement, the generalized robustness and the geometric measure of entanglement;

(ii) the entanglement of superpositions will be generalized to the multipartite case and to several entanglement quantifiers;

(iii) a recently proposed Bell inequality for continuous-variable (CV) systems will be used to extend, for the CV scenario, the Peres' conjecture that bound entangled states admit a description in terms of hidden variables.

(iv) a proposal to probe the geometry of the set of separable states will be made. This approach is able to find singularities in the border of this set, and those are reflected in the entanglement properties of condensed matter, atomic, and photonic systems. An experiment involving entangled photons coming from parametric down conversion will be described to illustrate the theoretical results;

(v) the decay of entanglement of generalized N-particle GHZ states interacting with independent reservoirs will be investigated. Scaling laws for the decay of entanglement and for its finite-time extinction (sudden death) are derived for different types of reservoirs. The latter is found to increase with the number of particles. However, entanglement becomes arbitrarily small, and therefore useless as a resource, much before it completely disappears, around a time that is inversely proportional to the number of particles. The decay of multi-particle GHZ states will be shown to generate bound entangled states;

(vi) and finally, the entanglement properties of particles in a non-interacting Fermi gas are studied. Since there is no interaction among the particles, this entanglement comes solely from the statistical properties of the particles. It will be shown how the way we detect the particles changes their entanglement properties. Additionally a realistic proposal to convert identical particle entanglement of fermions in a quantum well into useful photonic entanglement will be given.


Friday, October 17, 2008, 11:00h. Auditorium ICFO.

Thesis Advisor: Prof. Antonio Acín