Highly entangled multiqubit states and optimal time evolution

Resumen

This thesis is devoted to the study of multipartite entanglement and its relationship with the problem of optimal time evolution. We introduce several multipartite entanglement measures and study their main properties paying special attention to the characterization of highly entangled states of multiqubit systems. We find the explicit expression for maximally entangled states in systems composed up to seven qubits, which are also robust under the action of several decoherence processes. We also give evidences supporting the fact that the transition time associated with the evolution between two arbitrary initial and final quantum states is usually shorter for systems characterized with a high degree of entanglement. We finally propose a new methodology to optimize the design of quantum algorithms, considering the minimization of the real physical time needed to implement them.