Entanglement Swapping And Entanglement Concentration In Bose-Einstein Condensates

Quantum information and quantum computation developed quickly in the last decade is the outcome that quantum mechanics and the information sciences combine together and the notable feature of this subject is that the carriers of information is quantum sates. It aims to accomplish the storage, transfer, transmission and process of information by means of the coherence of quantum states. Quantum entanglement as a basic source of quantum communication is one of the most important subject, and also, the strangest part of quantum information. In quantum information, the processing of information depends on quantum sate and its evolution, while quantum entangled states certainly is the most important kind among all kinds of quantum states. As is well known, the quality and quantity of the quantum entanglement degrade in the progress of the transmission of information by virtue of the existence of the decoherence. So we must enhance the entanglement using the entanglement swapping and concentration.In this paper, we study chiefly the entanglement swapping and concentration in multi-pair trapped Bose-Einstein condensats and the influence which results from the change of the pairs of the initial states and the atom number that the initial sates obtain on entanglement of the entanglement swapping sate.In the second chapter, we introduce the basic theory about Bose-Einstein Condensation and correlative knowledge of atom trap. In the third chapter, we introduce some methods about measuring entanglement after having introduced simply the basic concept of the quantum entanglement. In the forth chapter, we propose a scheme of entanglement swapping and concentration in a system consisting of multi-pair Bose-Einstein condensates. Entanglement swapping is accomplished by using interference-pattern joint measurements and detecting the total number of condensed atoms leaking out of relevant traps and entanglement concentration is realized by choosing the appropriate initial entangled states. Moreover, we have found that the maximum entan-glement in the region of entanglement condeasatieHtof the entangled swapping state increases with the enhancement of the initial entangled pairs and the entangled degree of the entanglement swapping state increases with the enhancement of the atom number of the initial sates when it is eVen. In the fifth chapter, we perform entanglement swapping and concentration in multi-pair two-state BECs. We hate found the general expression of the swapping states from which we can see the condition when the swapping sates reach the maximum entanglement and that entanglement concentration rej^n is larger when the initial entangled pairs have the same atom number than the concentration region when the initial entangled pairs have different atom number.