Nonlocality and Game in Quantum Information

• Main Authors: Li-Yi Hsu, 徐立義
• Other Authors: Yih-Yuh Chen
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/28627119134302679003

博士 === 國立臺灣大學 === 物理學研究所 === 90 === Although mysterious entanglement in quantum theory still makes physicists confused, it plays a very important role in the promising scenario of quantum information. However, there is an essential issue for the potential applications: how to maintain the purified entangled states under the systematic and random noise? At first, we propose a scheme of entanglement purification via entanglement swapping or quantum repeater. The scheme needs less classical communication to achieve the optimal purifying. We also prove that this scheme can also reach the optimal success probability. However, in considering a long quantum channel with quantum repeaters, the BB84 protocol of quantum key distribution is dramatically changed. Although both key-makers have no initial information, they can still make a secret key. Only one of the repeater managers knows initial information. They three hold incomplete information. If one of key-makers reveals all his/her information, the other two can make a secret a key Secondly, we can apply our purification scheme to the optimal probabilistic quantum teleportation in a two-level case, which is equivalent to extracting the wanted but unknown qubit from the present qubit. In this dissertation, we consider the general extraction in the n-level case. We give a rigorous argument that, under some specific collective unknown-independent unitary transformation U on this n-level qudit and auxiliary qubits as probe, the maximal probability to successfully extract the wanted qubit can be reached. Moreover, we also prove that the maximal extraction probability is unchanged by adding more probe qubits. Finally, we consider a quantum game without classical analogy. We think three qubits, which states are nonorthogonal but equally overlapped to one another, as poker cards. One takes one of them and the other two cards. Their tasks are to know what Bob has at hand as possible as they can by measuring their own cards respectively. The result shows that Alice may know more than Bob because of the quantum effect.