Dispensing of quantum information beyond no-broadcasting theorem -- is it possible to broadcast anything genuinely quantum?

TL;DR

This paper explores the boundaries of the no-broadcasting theorem in quantum information, showing that under certain restrictions, broadcasting can be possible beyond the standard limitations, with some cases requiring commutativity.

Contribution

It generalizes the no-broadcasting theorem by considering restricted sets of states and measurements, revealing new conditions where broadcasting is or isn't equivalent to commutativity.

Findings

Broadcasting is equivalent to commutativity in some restricted cases.

In other cases, broadcasting can occur without commutativity.

The results expand understanding of quantum information limitations.

Abstract

No-broadcasting theorem is one of the most fundamental results in quantum information theory; it guarantees that the simplest attacks on any quantum protocol, based on eavesdropping and copying of quantum information, are impossible. Due to the fundamental importance of the no-broadcasting theorem, it is essential to understand the exact boundaries of this limitation. We generalize the standard definition of broadcasting by restricting the set of states which we want to broadcast and restricting the sets of measurements which we use to test the broadcasting. We show that in some of the investigated cases broadcasting is equivalent to commutativity, while in other cases commutativity is not necessary.