Quantum Information Theory is an emerging field that aims to use the particular features of Quantum Mechanics to perform communication protocols whose realization would be impossible in a classical world. Among its main applications, one could cite quantum cryptography, teleportation, dense coding…

Most of these protocols were initially conceived to be implemented in discrete systems. Unfortunately, the control and manipulation of these systems is still a challenge. On the other hand, Quantum Optics is a well established discipline: linear optical elements, together with optical parametric amplifiers and photodetectors allow to implement a wide range of operations with high precision in infinite dimensional quantum systems. In this dissertation, I will study the possibilities and limitations offered by infinite dimensional Hilbert spaces to perform quantum information tasks.

After a brief introduction, I will analyze the problem of providing privacy by means of Gaussian operations. In particular, I will prove that, for a big family of continuous variables quantum cryptographic protocols, the two honest parties can always assume that the attack performed by a possible eavesdropper consists on a Gaussian interaction. Consequently, I will be able to determine the security regions of the squeezed state protocol and the coherent state protocol.

Then I will consider the state estimation of Gaussian states distributed according to a Gaussian probability distribution. I will derive a general upper bound on the maximum fidelity attainable, as well as some conditions that indicate when such bound is tight. We will see that these conditions appear quite often. Moreover, if that is the case, the best strategy to distinguish the states makes use of Gaussian operations and is, therefore, easy to implement experimentally. These results have immediate applications in the calibration of optical devices.

Finally, I will forget about continuous variables systems and try to look for general limitations of the Quantum Mechanical paradigm. The ability to perform communication tasks depends mainly on the strength of the correlations between distant parties. Therefore, I will study the set Q’ of quantum correlations that can be established between two or more space-like separated observers and provide a useful characterization for it. This characterization is important not only for quantum information applications, but also from a fundamental point of view, as it gives us tools to disprove Quantum Mechanics in favor of more general theories. Besides, a slight modification of the procedure allows to obtain a systematic method to calculate the maximum violation of a linear Bell inequality compatible with Quantum Mechanics.


Friday, 14th of December, 12:00h. Conference Room

Thesis Advisor: Prof. Antonio Acín