Optimal Cloning of Symmetric Pure States on Bloch Sphere’s Equator

• Main Authors: Kuan-Mou Lai, 賴冠謀
• Other Authors: Hsien-Tung Huang
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/17753844462843401783

碩士 === 國立東華大學 === 應用物理研究所 === 98 === We study the optimal cloning transformation for a set of n pure states symmetrically distributed on a Bloch sphere equator, and derive the corresponding optimal fidelities, where the output of the cloner is required to be supported on the symmetric subspace. We find that the optimal cloning of an arbitrary finite number n of quantum pure states that are symmetrically distributed on the equator of the Bloch sphere is equivalent to optimally cloning the whole equator of the Bloch sphere. This shows that fidelity is the same for any equatorial qubit, i.e., it does not depend on the value of the phase. We also give the explicit form of a optimal cloning transformation for the case n = 2.