Broadcasting Quantum Fisher Information

TL;DR

This paper explores the possibility of broadcasting quantum Fisher information, a measure of statistical distinguishability, showing it cannot be cloned but can sometimes be broadcast, bridging classical cloning and quantum no-broadcasting principles.

Contribution

It introduces the concept of broadcasting quantum Fisher information, demonstrating its potential to be broadcast even when quantum states are non-commuting, unlike traditional quantum information.

Findings

Quantum Fisher information cannot be cloned.

Quantum Fisher information can be broadcast under certain conditions.

The work bridges classical cloning and quantum no-broadcasting principles.

Abstract

It is well known that classical information can be cloned, but non-orthogonal quantum states cannot be cloned, and non-commuting quantum states cannot be broadcast. We conceive a scenario in which the object we want to broadcast is the statistical distinguishability, as quantified by quantum Fisher information, about a signal parameter encoded in quantum states. We show that quantum Fisher information cannot be cloned, whilst it might be broadcast even when the input states are non-commuting. This situation interpolates between cloning of classical information and no-broadcasting of quantum information, and indicates a hybrid way of information broadcasting which is of particular significance from both practical and theoretical perspectives.