Cloning and Broadcasting in Generic Probabilistic Theories

TL;DR

This paper establishes broad no-cloning and no-broadcasting theorems for a wide class of probabilistic models, including quantum and super-quantum theories, based on no-signaling and state distinguishability.

Contribution

It generalizes the no-cloning and no-broadcasting theorems to all non-classical finite-dimensional probabilistic models satisfying no-signaling, providing a natural and self-contained proof.

Findings

Cloning and broadcasting are only possible for states within a simplex of distinguishable, cloneable states.

Theorems apply to quantum and super-quantum models with stronger-than-quantum correlations.

A set of states is broadcastable iff it lies in a simplex with vertices that are distinguishable and cloneable.

Abstract

We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially {\em any} non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well as models supporting ``super-quantum'' correlations that violate the Bell inequalities to a larger extent than quantum theory. The proof of our no-broadcasting theorem is significantly more natural and more self-contained than others we have seen: we show that a set of states is broadcastable if, and only if, it is contained in a simplex whose vertices are cloneable, and therefore distinguishable by a single measurement. This necessary and sufficient condition generalizes the quantum requirement that a broadcastable set of states commute.