Quantum n-level qudit purification scheme

• Main Authors: Hsin-Pin Lo, 羅信斌
• Other Authors: Li-Yi Hsu
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/14084300117906595652

碩士 === 中原大學 === 應用物理研究所 === 94 === Abstract Due to the promising potential causing revolutionary advance involving computation, communication and cryptography, quantum information science (QIS), as an emerging and cross-disciplinary subject has been rapidly expand and began its explosive growth since the early to mid 1990’s. Therein, quantum entanglement plays an important role in QIS. Now, entanglement is regarded as a key resource in quantum communication protocols, such as quantum key distribution, dense coding and teleportation. In the physical realization of the above protocols, an ensemble of maximally entangled states should be prepared and shared in advance for the two distant parties. However, an essential obstacle comes form decoherence. The interaction between quantum bits (qubits) and the environment generally disturbs and even destroys the entanglement. Therefore, entanglement purification on the unknown mixed states is necessary before the implementation of any entanglement-based quantum communication protocol. In this thesis, a scheme of how to purify n-level bipartite maximally-entangled states is proposed. This scheme consists of three steps in each round. At the first purification step, one partite performs the local Hadamard transformation and the other party the corresponding inverse transformation. At the second step, the bilateral controllednot operations are performed. At the last step, the target pairs are measured, if the outcome is coincided, the controlled pairs should be kept for the next round; otherwise, the controlled pairs and target pairs both should be discarded. These three steps should be performed repeatly and finally maximally entangled states can be accessed. We also numerically simulate the proposed purification scheme. In brief, the results show that the proposed scheme can purify the n-level bipartite maximally-entangled states, where n can be 3, 4, 5, 6 and 7, if the initial fidelity is larger than 1/n. Moreover, the final fidelity of the intended maximally entangled states can reach 1 after about ten rounds. On the other hand, the theory indicates that the n-level bipartite mixed states are inseparable if the fidelity of some maximally entangled state is larger than 1/n. Therefore, our simulation implies that the purification of quantum entanglement can be achieved for any inseparable mixed states. In addition, some specific cases are discussed. Especially, in the n=3 case, the proposed purification scheme can fail in some special initial fidelity distributions. The criteria of successful purification can be derived analytically.