Unbounded Bell violations for quantum genuine multipartite non-locality

Abstract

The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However, the multipartite setting entails a more complex classification in which different notions on non-locality can be established. In particular, genuine multipartite non-local distributions apprehend truly multipartite effects, given that these behaviours cannot be reproduced by bilocal models that allow correlations among strict subsets of the parties beyond a local common cause. We show here that, while in the so-called correlation scenario the relative violation of bilocal Bell inequalities by quantum resources is bounded, i.e. it does not grow arbitrarily with the number of inputs, it turns out to be unbounded in the general case. We identify Bell functionals that take the form of non-local games for which the ratio of the quantum and bilocal values grows unboundedly as a function of the number of inputs and outputs.

Genuine multipartite entanglement in noisy quantum networks highly depends on the topology

“…To bound their winning probability we will use the same techniques as in Refs. [32,41]. Recall that, for the bipartite game, the questions are cosets of H in the group {0, 1} v , which can be thought of as u ⊕ H for Alice and u ⊕ z ⊕ H for Bob (where u ∈ {0, 1} v is sampled uniformly and z ∈ {0, 1} v is sampled bitwise independently with noise η), and the answers are elements of the question cosets.…”

“…(55) guarantee that the edge with the isotropic state is entangled but nonsteerable [31]. Finally, using the ideas of [32], we extend the Bell inequality used to prove bipartite superactivation in [17,33] to a multipartite one in order to show that τ (p) ⊗k is GMNL for a large enough k.…”

Asymptotic Survival of Genuine Multipartite Entanglement in Noisy Quantum Networks Depends on the Topology

“…( 6) guarantee that the edge with the isotropic state is entangled but nonsteerable [46]. Finally, using the ideas of [47], we extend the Bell inequality used to bipartite superactivation in [22,48] to a multipartite one in order to show that τðpÞ ⊗k is GMNL for a large enough k.…”