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

Abstract

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.

Figures (2)

• Figure 1: Modifications of the standard bipartite single-round Bell scenario, aiming at device-independent entanglement detection of the source $\rho_{AB}$ (blue). The auxiliary devices (black) are untrusted, but assumed to follow quantum mechanics. (a) Sequential-measurement scenario: each party applies a sequence of instruments on the received system. (b) Network-embedding scenario: the source $\rho_{AB}$ is embedded in a larger network with two additional independent sources. (c) Broadcasting scenario: each party applies a local operation that splits the received system into two subsystems, $A_1,A_2$ and $B_1,B_2$.
• Figure 2: a) Honest isometry in the broadcasting network enabling the device-independent entanglement detection of any state $\rho_{AB}$. Each local isometry routes the incoming system $A$ ($B$) to $A_1$ ($B_1$), while distributing a maximally entangled state $\Phi^+$ between $A_1$ ($B_1$) and $A_2$ ($B_2$). b) Subsystem dictionary for Alice after the Bowles self-test (Eq. \ref{['eq: ST']}). Both physical systems $A_1,A_2$ split into three subsystems. The qubits $A_1',A_2'$ carry an EPR pair $|\Phi^+\rangle$. The remaining systems are in a state $\ket{\xi}=\sum_{k=0}^1 \ket{\xi_k}_{\bar{A}_1 \bar{A}_2 BE}\ket{kk}_{A_1"A_2"}$, where the flag qubits $A_1",A_2"$ label the transposition-branch, while the systems $\bar{A}_1, \bar{A}_2$ collect the remaining degrees of freedom. Up to transposition controlled by the flag qubit $A_2"$, the measurement device ${\tt A}_2^{(a_2|x_2)}$ performs the three Pauli measurements of the qubit $A_2'$. Certification of this measurement and of the EPR pair provides a device-independent extracted qubit register $A_1'$, which serves as a certified quantum subsystem for subsequent entanglement-detection and self-testing arguments in the broadcast network. c) The extraction instrument $\{\mathcal{E}_A^{(a_1)}: A \to A_2' A_2"\}$, producing two qubits and a classical outcome $a_1$ from the input system $A$.

Theorems & Definitions (1)

• Lemma 1: The Bowles self-test, Lemma 1 in bowles2018vsupic2023quantum