Distillation Schemes For Quantum Entanglement And Nonlocality

Quantum entanglement and nonlocality are important resources for quantum information processing, meanwhile they are fundamental concepts in quantum information science. Quantum entanglement plays an important role in quantum teleportation, quantum communication, quantum computation and so on, and nonlocality plays a key role in the area of quantum cryptography. In the process of quantum information processing, in order to guarantee the quality of quantum communication states with higher degree of entanglement are needed, so we need to conduct distillation operation on the practically available non-maximally entangled states. Via local operations and classical communications one can improve entanglement and approach the maximally entangled state. Being similar to entanglement distillation, nonlocality distillation needs local operation too, but there is still difference between entanglement distillation and nonlocality distillation. During the process of distillation, local operations and classical communications are needed for entanglement distillation, but the classical communication is not permitted for nonlocality distillation, and only local operations are needed.In this thesis, we focus on entanglement distillation and nonlocality distillation. The main research work is as follows:1. We proposed a scheme for enhancing and expanding remote photonic entanglement via local filtering operations, and the mixed entangled state to be distilled is the Collins-Gisin state. Firstly, we designed the main entanglement distillation process with the help of auxiliary photons and non-destructive measurement; Secondly, we found that the garbage states can be redistilled; Finally, through comparing the fidelities of the states before and after the distillation process we conclude that the entanglement can be enhanced by adjusting the related parameters properly.2. We proposed the distillation scheme for multipartite entanglement by local filtering operations. With the help of positive operator valued measures(POVMs), the entanglement distillation of amplitude damped GHZ state and the amplitude dampedW state can be distilled. We considered the cases of two-POVM-based scheme and three-POVM-based scheme, and found that distillation can be realized in both of these two cases. In addition, we compared the nonlocalities of the states before and after the distillation, and found that the distillation process can reveal genuine tripartite nonlocality of the noisy GHZ states and noisy W states.3. Two-physical realization schemes for quantum nonlocality distillation were designed in cavity QED system. Based on the cavity-assisted interaction between atoms and light pulses and the detuned interaction between atoms and single-mode cavity field, two schemes were proposed to realize the key operation of nonlocality distillation--module 2 addition, and thus the nonlocality distillation was realized.