Research On The Manipulations Of Nonlocal Correlations Within Nonsignaling Theory

The quantum correlations have amazing abilities in information processing, which is due to the special properties of quantum mechanics (QM). Entanglement and nonlocality are two major aspects of quantum correlations. Quantum entanglement plays important roles in many quantum information processes, such as teleportation and key distribution. With the investigation on quantum correlations, the significance of nonlocal correlations in the information field has been recognized. The fact that measurements on two spatially separated entangled particles can give a correlation, which can not satisfy reality and locality simultaneously, is well known as quantum nonlocality. The degree of nonlocality for some state can be measured by the state’s violation value of different types of Bell inequality. Recent results showed that, in general nonsignaling theory, quantum nonlocality is bounded and can not reach its algebra maximum, and the correlations beyond quantum nonlocality exists and is usually called as post-quantum nonlocality. Nonlocal correlations can make communication complexity trivial. Computation and distillation based on nonlocality are all allowable. In general, more nonlocality the resource has, superior performance it shows in information processing. So, in this thesis, nonlocality distillation within nonsignaling theory is discussed detailedly. In addition, nonlocality is a usual analog of entanglement in our study, such as, nonlocality swapping is the analog of entanglement swapping, but it is different from entanglement in many aspects. So nonlocality swapping is another main topic of this thesis.Several more efficient and more universal nonlocality distillation protocols appeared after the original one. The only existing nonlocality swapping scheme is based on a coupler, and does not work in multipartite system. Most of the existing nonlocality distillation and swapping protocols are only working for bipartite binary systems, and the simple generalizations of these proctocols to the multinary systems does not work. So we need to design new wiring manners and coupler of the nonlocal boxes. Herein this thesis, we generalized the distillation of nonlocality to multipartite and multi-dimensional cases, and multipartite nonlocality swapping was discussed too. The major contents of the thesis are organized as follows:1. Nonlocal boxes within (?) nonsignaling theory and their nonlocality measure. Starting from the existing Bell inequalities, we gave the explicit forms of the Bell inequalities. Many kinds of nonsignaling boxes are presented and the corresponding degrees of nonlocality are measured by the relevant Bell-type inequalities.2. The nonlocality distillation protocols of bipartite multi-nary boxes. The distillation protocols for bipartite binary boxes cannot distill the bipartite multinary boxes, so we designed new distillation protocols for bipartite multi-nary boxes.3. Nonlocality distillation for multipartite multi-nary boxes. We found that when used on the tripartite binary boxes, the bipartite binary distillation scheme does not work fine, so we designed a new optimal scheme for the distillation of tripartite binary boxes.4. Multipartite nonlocality swapping. Based on the coupler of the only existing bipartite nonlocality scheme, we designed a new swapping scheme for generating multipartite nonlocal correlations. We also tried to design a brand new coupler so that the swapping process can be greatly simplified.