State The Nature Of Quantum Entanglement In Quantum Information Science Applications

Quantum information theory is a new interdiscipline and it is based on a new quantum resource, namely the so called quantum entanglement. Many novel quantum-information tasks, that cannot be carried out by classical resources, have been theoretically or experimentally realized in recent years. For example, the quantum computer has been proved to have the ability to manage some tasks in a short time, while the latter cannot be done on a classical computer due to the deficient algorithms. In addition, the quantum cryptography can protect the information in a new way that cannot be eavesdropped by means of classical attack. These applications imply the importance of entanglement, and the existence of entanglement has caused the deeper understanding of the essence of quantum mechanics and its basic hypothesis. Extensive research on entanglement has also been done in recent years.In this dissertation, I investigate the use of entanglement in quantum in-formation theory in terms of three main aspects, in each of which I have made several different works. That is,1. Quantum communication and quantum cloning.I study the probabilistic implementation of nonlocal gates and improve its efficiency by using the non-maximally entangled states. I also investigate the universality of quantum channel in remote state preparation and it estimates the minimum number of necessary channels for all qubits. I show that no uni-versal quantum cloning machine exists that can broadcast an arbitrary mixed qubit with a constant fidelity. In this sense, I present different kinds of depen-dent quantum cloning machines for mixed states. I also propose the asymmetric quantum telecloning scheme for multiqubit states with an optimal fidelity.2. Classification of multipartite entanglement.I propose the range criterion that is a sufficient and necessary condition sat-isfied by two multipartite pure states into each other under reversible stochastic local operations and classical communication. It leads to a systematic method for seeking all kinds of true entangled states in the 2 x M x N space, and it can also effectively distinguish them. I also use the range criterion to find out different families of a useful kind of multiqubit entangled states, namely the GHZ-W-type states. Many states that are experimentally realizable belong to this class of states. I show that the classification is related to the enumerative combinatorics and also give the condition on which two GHZ-W-type states are totally equivalent.3. Entanglement detection and entanglement measures.I introduce a feasible method of constructing the entanglement witness that detects genuine multiqubit entanglement in the vicinity of a given pure multiqubit state. Our method can establish effective witnesses for experiments and for other kinds of states. I present a new method of analytically deriving the entanglement of formation of the bipartite mixed state by means of the optimal decomposition families of states. Our method also leads to many new results on the additivity of entanglement of formation as well as entanglement cost. I also prove that the bipartite rank three entangled states are distillable under local operations and classical communication. So there is no rank three bipartite bound entangled state. Moreover, it leads to some families of rank four entangled states that are distillable. I also show that our result is independent of the expectant fact that there exists bound entangled Werner state.