Preparation, Application And Nonlocality Of Quantum Entangled States

Quantum information science has emerged as one of the most exciting scientific developments of the past twenty years.The new technological prospects of quantum information in quantum cryptograph,quantum communication and quantum computation attract not only physicists but also researchers from other scientific communities, mainly mathematicians,computer scientists and electrical engineers.Quantum entanglement is a special quantum mechanical resource that plays a key role in many applications of quantum computation and quantum information,it is a key element in effects such as quantum teleportation,fast quantum algorithms,and quantum error-correction. As a result,there is a thriving research community in finding principles which govern its manipulation,utilization and its quantitative and qualitative description,This thesis is a contribution to the analysis on the preparation,application and nonlocality of the entangled states.The structure of this thesis is as follows:Chapter 1 is the exordium.I simply introduce the general knowledge about quantum information and some important applications based on quantum entanglement.In Chapter 2 I review basic aspects of entanglement including its mathematical description,inseparable criterion and entanglement measure.In Chapter 3 I briefly introduce several common quantum entangled states and study their properties and applications.In Chapter 4 an attempt is made to propose a electronic linear optical scheme for the teleportation and entanglement concentration via entanglement swapping based on charge detection.I also prove that this method is useful in generating entangled states such as GHZ states,W states,and cluster states using fermionic polarizing beam splitters and single spin rotations assisted by parity check on the fermionic qubits.Our scheme is nearly deterministic(i.e.,with 100%success probability) and does not need the joint Bell state measurement required in the previous schemes.In Chapter 5 I propose a method of generating the cluster-type entangled coherent states(CTECS) and the W state through the cavity-electron interaction.Furthermore, I investigate the nonlocal properties of the generated CTECS and the time evolution of the electron-cavity system involving cavity decay.In Chapter 6,Greenberger-Horne-Zeilinger(GHZ) theorem constitutes that there is a set of mutually commuting nonlocal observables with a common eigenstate on which those observables assume values that refute the attempt to assign values only required to have them by the local realism of Einstein,Podolsky,and Rosen(EPR).It is known that there is only one form of the GHZ-Mermin-like argument with equivalence up to a local unitary transformation.However,we show that there are eight distinct forms of the Greenberger-Horne-Zeilinger(GHZ) argument for the four-qubit cluster state and forty eight distinct forms for the five-qubit cluster state in the case of the onedimensional lattice.The proof is obtained by regarding the pair qubits as a single object and constructing the new Pauli-like operators.The method can be easily extended to the case of the N-qubit system and the associated Bell operator are also discussed, on which only cluster states assume its maximum value.Consequently,we present a complete construction of the GHZ theorem for the cluster states of N-qubit in the case of the one-dimensional lattice.Summary and some open problems are given in Chapter 7.