Physics – Quantum Physics
Scientific paper
2001-08-03
Physics
Quantum Physics
11 pages, RevTex, 2 eps figures. The paper is reorganized. Three references are added. The notion of the relative error is bet
Scientific paper
We propose new optimality criterion for the estimation of state-dependent cloning. We call this measure the relative error because the one compares the errors in the copies with contiguous size taking into account the similarity of states to be copied. A copying transformation and dimension of state space are not specified. Only the unitarity of quantum mechanical transformations is used. The presented approach is based on the notion of the angle between two states. Firstly, several useful statements simply expressed in terms of angles are proved. Among them there are the spherical triangle inequality and the inequality establishing the upper bound on the modulus of difference between probability distributions generated by two any states for an arbitrary measurement. The tightest lower bound on the relative error is then obtained. Hillery and Buzek originally examined an approximate state-dependent copying and obtained the lower bound on the absolute error. We consider relationship between the size of error and the corresponding probability distributions and obtain the tightest lower bound on the absolute error. Thus, the proposed approach supplements and reinforces the results obtained by Hillery and Buzek. Finally, the basic findings of investigation for the relative error are discussed.
No associations
LandOfFree
Some bounds for quantum copying does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Some bounds for quantum copying, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some bounds for quantum copying will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-244142