Practical Quantum Broadcasting

TL;DR

This paper explores the limits of quantum broadcasting, introducing approximate and probabilistic methods to overcome no-go theorems, and demonstrates practical protocols for distributing quantum information efficiently.

Contribution

It develops new approximate and probabilistic quantum broadcasting protocols with analyzed sample complexities, challenging existing no-go theorems and enabling efficient quantum information distribution.

Findings

Approximate virtual broadcasting reduces sample complexity overheads.

Probabilistic protocols face stronger no-go restrictions for 1-to-2 broadcasting.

Practical 1-to-6 virtual broadcasting is achievable for qubits.

Abstract

Incorporating sample efficiency, by requiring the number of states consumed by broadcasting does not exceed that of a naive prepare-and-distribute strategy, gives rise to the no practical quantum broadcasting theorem. To navigate this limitation, we introduce approximate and probabilistic virtual broadcasting and derive analytic expressions for their optimal sample complexity overheads. Allowing deviations at the receivers restores sample efficiency even in the 1-to-2 approximate setting, whereas probabilistic protocols obey a stronger no-go theorem that excludes all sample efficient 1-to-2 implementations for arbitrary dimension and success probability. Rather counterintuitive, this obstruction does not persist at larger receiver numbers: for qubit systems, practical 1-to-6 virtual broadcasting becomes attainable. These results elevate sample complexity from a technical constraint to a defining operational principle, opening an unexplored route to the efficient distribution of quantum information.