Creation And Purification Of Quantum Entangled States

Quantum Information is a new subject, which is the combination of QuantumMechanics and Information Science. Because of its potential application inrevolutionizing the methods by which we manipulate information, QuantumInformation has gained more and more attention recently.Entangled states play a crucial role in Quantum Information. One can say,Quantum Information can not exist without entanglement. Because of itsnon-locality feature, entangled states become very important physical resources inquantum information processing. As the basis of Quantum Information, entangledstates find its significant applications in quantum communication and quantumcomputation. The research on entangled states includes generation of entangledstates, distribution of entangled resources and manipulation of entangled states, etc.It is well known that, decoherence of quantum system is a bottleneck for therealization of quantum information processing and quantum computation. Thus, inthis PhD thesis, we carried out our research work on the generation of entangledstates and the purification of non-maximally entangled states (includingconcentration of pure non-maximally entangle states and purification of mixedentangled states):1. Generation of ionic entangled states via linear optics. In the scheme, therelative phase problem inherent in the previous schemes has been avoided; Thephoton to be detected is the input photon, which is easier to be dectected than thescattered photon from the ions; The scheme can generate pure maximally entangledstates not only from product initial states but also from the mixed entangled initialstates.2. Based on the large detuned interaction between aΛ-type three-level atomand a coherent optical field, we propose the scheme for the generation of multi-atomentangled states and multi-cavity entangled states. The unique advantage of this scheme is that it can realize the controlled-not operations, from atoms to coherentfields, from coherent fields to atoms, from one atom to another, and from onecoherent field to another. The feasibility of the current scheme is aso discussed indetail.3. General implementation of entanglement concentration for non-maximallyentangled states of arbitrary dimension system and its physical implementation. Theresult shows that, entanglement concentration for the unknown non-maximallyentangled states can be realized by generalized controlled-not operations in arbitrarydimension system; the quantum-state-discrimination-based entanglement swappingcan be used to realize the concentration of known non-maximally entangled states.Here, rather than the remote entanglement we use the local entanglement, which canbe prepared in an easier way than the remote entanglement, to enhance the remoteentanglement; Based on generalized measurement, a general method for theconcentration of a known non-maximally entangled state for arbitrary dimensionalsystem is proposed only by introducing a qubit ancilla, which will greatly simplifythe total concentration process.4. Entangement purification for unknown mixed entangled states. Anentanglement purification scheme for arbitrary unknown mixed entangled ionicstates is proposed by using linear optical elements. The main advantage of thescheme is that the controlled-not operations inherent in the original entanglementpurification scheme are avoided here, which enhances the feasibility of the schemegreatly. As far as we know, it the first physical scheme for the entanglementpurification of mixed ionic entangled states; The entanglement purification formixed entangled coherent states and mixed entangled atomic states have beenproposed by using the large detuned interaction between aΛ-type three-level atomand a coherent optical field.5. The feasibility of the generation and purification scheme for ionic system vialinear optical elements is discussed in detail. We conclude that the scheme is wellwithin current technology.6. A teleportation scheme for unknown atomic states is proposed in cavity QED. The Bell state measurement in the teleportation process has been converted into theproduct of the single measurements on qubits in a rather easy way, and the successprobability can reach 1.0. In addition, the current scheme is insensitive to the cavitydecay and thermal field, which enhance its experimental feasibility greatly.