Quantum Entanglement In Quantum Information

Quantum information is a kind of new information technology which was developed in the past two decades. Quantum entanglement, which is an important physical resource in quantum information, plays a critical role in it. Bipartite entanglement and multipartite entanglement can complete some tasks which cannot be completed in classical information theories. Quantum teleportation, dense coding, quantum cloning, quantum cryptography, and quantum parallel computing are just a few examples. In recent years, as more and more research has been done on the phenomenon of quantum entanglement, significant advances have been made in this area and many important conclusions have been drawn. However, we still cannot fully understand its nature. For example, given a quantum state, how to determine whether it is entangled? Furthermore, when a state is an entangled one, then how to measure its degree of entanglement? A lot of questions need to be tackled. This paper mainly focuses on introducing the following aspects of quantum entanglement.I. Introducing the concept of entanglement state, defining separable state and entanglement state, and giving some commonly used methods of judgment.II. Discussing some common measurements of entanglement, with three-tangle and four-tangle being the center of research:(1) First, constructing a family of rank-n (n=5,6,7,8) three-qubit mixed state; then giving an explicit expression of the three-tangle and the optimal decompositions for all these states; and finally, verifying the CKW inequation.(2) Studying a five-qubit entanglement measurement:five-tangle, and a six-qubit entanglement measurement:six-tangle, with the methods and conclusions of four-tangle study being the basis.III. Introducing three-tangle of assistance:(1) Studying the three-tangle of assistance for mixed three-qubit states, including a generalized GHZ state, a|000)+b|111>,and a generalized W state, c|001)+d|010)+e|100>; presenting an explicit expression of the three-tangle of assistance and the corresponding optimal pure state decompositions; giving a lower bound on the assisted entanglement between two parties.