All Entangled States are Nonlocal and Self-Testable in the Broadcast Scenario

Entanglement and Bell nonlocality are known to be inequivalent: there exist entangled states that admit a local hidden-variable model for all local measurements. Here we show that this gap disappears in a minimal broadcast extension of the Bell scenario. Assuming only the validity of quantum theory, we prove that for every entangled state $ρ_{AB}$ there exist local broadcasting maps and local measurements such that the resulting four–partite correlations cannot be reproduced by any broadcast network whose source is separable across the $A|B$ cut. Thus, all entangled states are broadcast nonlocal in quantum theory. In addition, we show that all (also mixed) multipartite states can be broadcast-self-tested, according to a natural operational definition.

💡 Research Summary

The paper tackles a long‑standing gap in quantum information theory: while every Bell‑nonlocal state is necessarily entangled, the converse is false—there exist entangled mixed states (e.g., Werner states) that admit a local hidden‑variable model for all possible local measurements. The authors ask whether a modest modification of the standard bipartite Bell test can make all entangled states manifest nonlocal correlations without resorting to trusted devices or additional independent sources. Their answer is affirmative in the broadcast scenario, a minimal extension where each party locally “broadcasts’’ its subsystem to two new parties via a fixed quantum operation.

Broadcast network model.
Each original party (Alice A and Bob B) applies a local isometry (V_X) (X = A,B) that routes the incoming quantum system to an “output” subsystem (X_1) while simultaneously creating a maximally entangled pair (|\Phi^+\rangle) between an auxiliary qubit (X_{aux1}) and a second output subsystem (X_2). The global state after both isometries is \