Gaussian and non-Gaussian resources in Quantum Information

Abstract

This dissertation was carried out within the framework of the Quantum Information (QI). In particular, I have analyzed the main aspects: the protocol, the quantum states, the conditional measurements, and the decoherence. The protocol. I have studied the teleportation protocol, the entanglement swapping protocol, and the Bell’s inequality (which is the basis of some protocols such as the quantum cryptography). I have dealt with the maximization of the efficiency of each protocol, by acting on the generation of the appropriate quantum states. Starting from the known Squeezed Bell (SB) states that maximize the fidelity of teleportation, I have shown that even for the entanglement swapping protocol and for the violation of the Bell’s inequality, the SB states exhibit better performance than all the other continuous variable (CV) quantum states (for example squeezed vacuum states, subtracted photon squeezed states, added photon squeezed states, squeezed number states). Preparation of quantum states. I have presented an experimental scheme capable of generating, with good approximation, the SB states. I have identified a scheme that is based on conditional measures performed on ancillary quantum states. I have started to study an ideal scheme (free by inefficiencies and decoherence), obtaining the reproduction of the SB states. Then I have introduced the inefficiencies of detection, of the optical elements and of the conditional measurements. In the latter case, the scheme does not exactly reproduce the SB states, but tunable quantum states are obtained, which are very close to SB states. They exhibit a greater teleportation fidelity than all other realistic quantum states that we have analyzed. In addition, in collaboration with Prof. Salvatore Solimeno and Dr. Alberto Porzio of University of Naples "Federico II", I have studied (the work is still at a preliminary stage) the non-Gaussianity introduced by fluctuations in the pump amplitude of the Optical Parametric Oscillator(OPO) below threshold and with non-degenerate polarization. I have proved that such fluctuations lead to an increase of fidelity of teleportation with respect to the not fluctuating (and gaussian) case. Conditional Measurements. In the context of the QI, conditional measurements are used to prepare quantum states and to optimize the transfer of information, as required by the specific protocol. I propose a rather general formulation of the method of conditioning through ancillary measurements, in terms of the characteristic functions. I have considered the case of simultaneous measurements of single-photon, of homodyne detection, and of on/off type (via ideal and realistic POVM). Decoherence. The quantum properties are very sensitive to the interaction of the quantum systems with the external environment. For this reason, a part of this dissertation is devoted to analysis of the evolution of some quantum quantities under the action of the decoherence. In particular, I have studied how the effects of decoherence act on the following quantities: the purity, the quantum correlations, the content of information, the fidelity of teleportation of a coherent state, and the Bell’s inequality of a bi-partite Gaussian state that is transmitted through a realistic channel. I have added the experimental verification to the theoretical study, in collaboration with the University of Naples "Federico II" and under the guidance of Dr. Alberto Porzio and of Prof. Salvatore Solimeno. [edited by author]