Information cloning of harmonic oscillator coherent states and its fidelity

Abstract

We show that in the case of unknown {\em harmonic oscillator coherent states} it is possible to achieve what we call {\it perfect information cloning}. By this we mean that it is still possible to make arbitrary number of copies of a state which has {\it exactly} the same information content as the original unknown coherent state. By making use of this {\it perfect information cloning} it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We define the notion of a {\em Measurement Fidelity}. We show that this information cloning gives rise, in the case of $1\to N$, to a {\em distribution} of {\em measurement fidelities} whose average value is ${1\over 2}$ irrespective of the number of copies originally made. Generalisations of this to the $M\to MN$ case as well as the measurement fidelities for Gaussian cloners are also given.