We discuss the applications of Nuclear Magnetic Resonance (NMR) to quantum information processing, focusing on the use of quadrupole nuclei for quantum computing. Various examples of experimental implementation of logic gates are given and compared to calculated NMR spectra and their respective density matrices. The technique of Quantum State Tomography for quadrupole nuclei is briefly described, and examples of measured density matrices in a two-qubit I = 3/2 spin system are shown. Experimental results of density matrices representing pseudo-Bell states are given, and an analysis of the entropy of theses states is made. Considering an NMR experiment as a depolarization quantum channel we calculate the entanglement fidelity and discuss the criteria for entanglement in liquid state NMR quantum information. A brief discussion on the perspectives for NMR quantum computing is presented at the end.
