Test of Common Sense in Quantum Copying Process

TL;DR

This paper challenges the common belief that more prior information about input states improves quantum cloning quality, showing instead that factors like state denseness and the no-cloning theorem are more influential.

Contribution

It demonstrates that Shannon entropy-based prior information does not impact cloning quality, emphasizing the roles of no-cloning and state denseness.

Findings

Shannon entropy does not affect clone quality.

Denseness of input states is a key factor.

No-cloning theorem influences cloning limits.

Abstract

It is believed that the more we have {\it a priori} information on input states, the better we can make the quality of clones in quantum cloning machines. This common sense idea was confirmed several years ago by analyzing a situation, where the input state is either one of two non-orthogonal states. If the {\it a priori} information is measured by the Shannon entropy, common sense predicts that the quality of the clone becomes poorer with increasing $N$, where $N$ is the number of possible input states. We show, however, that the {\it a priori} information measured by the Shannon entropy does not affect the quality of the clones. Instead the no-cloning theorem and `denseness' of the possible input states play important roles in determining the quality. Specifically, the factor `denseness' plays a more crucial role than the no-cloning theorem when $N \geq 3$.