Advances in Entanglement and Quantum Information Theory

In this book, various types of entanglement have been discussed for systems start from a pure state or mixed states and many new features have been discovered. A general expression of the mixed state entanglement is obtained with the physical significance (with or without the diagonal approximation treatments). The particular advantages of using Shannon entropy are highlighted and the information entropy for different cases has been discussed. Also, the atomic inversion of cold atoms in a microcavity when its center-of-mass (CM) motion is described quantum mechanically is presented, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. It is shown that the spatial dependence of the atomic inversion is very sensitive to changes of the atomic CM motion, as well as the cavity length. For a three-level ultra-cold atoms, different behaviors in the atomic emission are demonstrated for the change in cavity length.