The Entangled States In Quantum Information Processing And Its Applications

Quantum information is a subject of the information processing tasks which could be accomplished using quantum system. It includes quantum computing, quantum commucation, entanglement, quantum cryptography, quantum correction and so on.This dissertation addresses entanglement and its application in quantum information processing. Here we present a hypothesis that any mixed state can be look on as a subsystem of entangled extended system. So we come to a conclusion that all the property of a mixed state oringin from the other part of the extended system's entanglement with it.We analysize possible oringination of a mixed state and show that any mixed state system can be regarded as a subsystem of a bigger extended system. It seems like a mixed state system because we can't observe the other part of the extended system. Generally there are infinite engtangled extended systems which are associated through a unitary operation corresponding to a mixed state system. We prove that all the entangled extended system are equivalence if only local operation or measurement is permmitted. So we can choose the most convenient method to construct the extended system.Then we show that to a local observer all the property and evolution of a mixed state system is equal as that of the extended system's subsystem. To all observable physical variable, such as average value, measurement outcome, Shannon entroy and Von Neuman entroy, what a local observer get is the same as what a collective observer get from the subsystem. At the same time the unitary operation of the mixed state system is consistent with corresponding unitary operation of the extedned system. Finally the operation-sum represent of the mixed state system can boil down to unitary operation of the extended system.The essence of entanglement is the correalations between the subsystem of the entangled state system while Von Neuman entroy is the most especial character in which a mixed state is diffeerent from a pure state. So there must be correlations between them. We prove that the Von Neuman entroy entroy of a mixed state and correlations of corresponding extended system is equivalence to describe a physical phenomenon.On the basis of our hypothesis that all the property of a mixed state oringin from the other part of the extended system's entanglement, we conclude that the property of mixed subsystem can be look on as a entanglement measure. As known the most important property of a mixed state relative to a pure state is that its Von Neuman entroy is nonzero. In a entangled state system, its subsystem is in mixed state. So we can take Von Neuman entroy as measure of entanglement. We define measure of entanglement in three-qubit system as follows.(1) The reason that one of the three-qubits is in mixed state is because the other...