Some bounds for quantum copying with multiple copies
Abstract
Description
We study the relative error of the state-dependent N=>L cloning. A copying transformation and dimension of state space are not specified. Only the unitarity of quantum mechanical transformations is used. The proposed approach is based on the notion of the angle between two states. Firstly, the notion of the angle between two states is discussed. The lower bound on the relative error of copying with multiple copies is examined. In addition, the lower bound on the absolute error is then studied. We compare the obtained bounds with the case of maximizing the global fidelity.
10 pages, ReVTeX, 2 figures. The paper is reorganized. To make the paper clearer, many parts are recast. Some lengthy fragments are deleted. The notion of the relative error is better motived. The figures are replaced. Three references are added. In sequence to quant-ph/0108014
10 pages, ReVTeX, 2 figures. The paper is reorganized. To make the paper clearer, many parts are recast. Some lengthy fragments are deleted. The notion of the relative error is better motived. The figures are replaced. Three references are added. In sequence to quant-ph/0108014