Quantum information entropy and multi-qubit entanglement

Abstract

The exciting new features of entanglement are burgeoning with revolutionary new advances in the areas of quantum communication, quantum information processing and quantum computing. We review recent theoretical studies and applications of pure and mixed states entanglement of trapped ions interacting with a laser field. After an introduction to the basic concepts of traditional entanglement measures and methodology, the main phenomena and observations of two-, three- and four-level systems are summarized. In particular, we explore the influence of the various parameters of these systems on the entanglement. The particular advantages of using atomic Wehrl entropy and Shannon entropy are highlighted. A general expression of the mixed state entanglement is obtained with the physical significance and without the diagonal approximation. Based on this result, we provide a general expression for the entanglement in a multi-level system. We show that the mixed-state and specific eigenstates of the two or three-level system posses remarkable entanglement properties that can reveal new insight into quantum correlations present in the multi-level models. Furthermore, we propose an intuitive picture of the behavior of mixed-state entanglement in the presence of the decoherence. After a short presentation of the entanglement measures of two qubits, each defined as an effective two-level system (negativity, Bures metric and concurrence) we discuss the general behaviors of the concurrence as a measure of entanglement. We identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the entanglement are influenced significantly when the multi-photon process is involved.