Quantum Information with Continuous Variable systems

TL;DR

This thesis explores quantum communication using Continuous Variable systems, emphasizing Gaussian states' advantages and limitations, and highlighting the potential of non-Gaussian states for enhanced quantum information tasks.

Contribution

It provides a comprehensive analysis of Gaussian and non-Gaussian states in CV quantum information, emphasizing their mathematical properties and practical applications.

Findings

Gaussian states enable high-precision quantum tasks with current optical technology

Non-Gaussian states may outperform Gaussian states in certain quantum information tasks

CV systems offer a rich framework for quantum communication and computation

Abstract

This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert spaces, thus involving a complex mathematical structure. A special class of CV states, are the so-called Gaussian states. With them, it has been possible to implement certain quantum tasks as quantum teleportation, quantum cryptography and quantum computation with fantastic experimental success. The importance of Gaussian states is two-fold; firstly, its structural mathematical description makes them much more amenable than any other CV system. Secondly, its production, manipulation and detection with current optical technology can be done with a very high degree of accuracy and control. Nevertheless, it is known that in spite of their exceptional role within the space of all Continuous Variable states, in fact, Gaussian states are not always the best candidates to perform quantum information tasks. Thus non-Gaussian states emerge as potentially good candidates for communication and computation purposes.