Some Research On Entanglement Witnesses And Quantum Clone Machines

Quantum entanglement and quantum cloning are two important concepts in quantum information, which have great practical application value. Based on reviewing and summarizing quantum entanglement witness and quantum clone machine, this paper does some further research and is divided into three chapters.In Chapter1, the research status and significance of quantum entanglement and quantum cloning are discussed briefly, and some basic knowledge of quantum information is introduced, such as linear algebra in quantum mechanics, inner products, outer products, tensor products, assumptions of quantum mechanics, pure states, mixed states and density operators. A brief description of this work is also introduced.In Chapter2, based on existing conclusions on entanglement witness of bipartite states, entanglement witnesses of bipartite quantum states are further discussed. First, in light of a decomposition of a self-adjoint operator, characterization of an entanglement witness is given, and some properties of entanglement witnesses are proved. An example is taken to illustrate the judgment of optimal entanglement witness. Finally, the optimal entanglement witnesses are discussed and a judgment of optimal indecompo-sable entanglement witness is presented.In Chapter3, the notion of1â†'3Wootters-Zurek quantum clone machine for pure states on C2is established based on the Wotters-Zurek quantum clone copying machine. The necessary and sufficient conditions of which input quantum states can be cloned by1â†'3Wootters-Zurek quantum-copying machine for the pure states on C2are introduced. By employing an example,{|0>,|1)|1â†'3Wootters-Zurek quantum clone machine for pure states on C2is illustrated, some properties of1â†'3Wootters-Zurek quantum clone machine for pure states on C2are discussed. The quality of cloning depends on the initial-state. Some relationships between the indexes of Dabc(i).(i=1,2,3) and D are obtained.