A new form of the no-cloning theorem for harmonic oscillator coherent states

TL;DR

This paper presents an alternative formulation of the no-cloning theorem specific to harmonic oscillator coherent states, highlighting limitations on amplification of unknown states and consistency with information cloning.

Contribution

It introduces a new formulation of the no-cloning theorem for harmonic oscillator coherent states, clarifying conditions for amplification and information cloning.

Findings

Unknown coherent states cannot be amplified.

Known coherent states can be amplified via a universal unitary process.

The formulation ensures consistency with prior information cloning proposals.

Abstract

We give an alternative formulation of the no-cloning theorem that applies to harmonic oscillator coherent states. It says that {\em unknown} single harmonic oscillator coherent states can not be {\em amplified}. Conversely it says that {\em known} harmonic oscillator coherent states can be directly amplified through an universal unitary process. It is also shown that such a formulation is needed for the consistency of {\em information cloning} proposed by us long ago.