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Superactivation of genuine multipartite Bell nonlocality from two-party entanglement

Markus Miethlinger, Riccardo Castellano, Pavel Sekatski, Nicolas Brunner

Abstract

Characterizing the relation between entanglement and Bell nonlocality is a long-standing open problem, notably challenging in the multipartite case. Here we investigate the effect of superactivation of genuine multipartite nonlocality. Specifically, we show that starting from multipartite states that feature only two-party entanglement (hence almost fully separable), it is possible to obtain GMNL in the many-copy regime. This represents the weakest possible resource for GMNL superactivation. On the technical side, we develop an efficient and practical criterion for certifying GMNL superactivation based on network entangled states, as well as a perfect parallel repetition result for the Khot-Vishnoi Bell game, which are of independent interest.

Superactivation of genuine multipartite Bell nonlocality from two-party entanglement

Abstract

Characterizing the relation between entanglement and Bell nonlocality is a long-standing open problem, notably challenging in the multipartite case. Here we investigate the effect of superactivation of genuine multipartite nonlocality. Specifically, we show that starting from multipartite states that feature only two-party entanglement (hence almost fully separable), it is possible to obtain GMNL in the many-copy regime. This represents the weakest possible resource for GMNL superactivation. On the technical side, we develop an efficient and practical criterion for certifying GMNL superactivation based on network entangled states, as well as a perfect parallel repetition result for the Khot-Vishnoi Bell game, which are of independent interest.
Paper Structure (13 sections, 4 theorems, 46 equations, 2 figures)

This paper contains 13 sections, 4 theorems, 46 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Setting the scene
  3. Superactivation of GMNL
  4. Methods
  5. GMNL from Fully Local state?
  6. Discussion and Outlook
  7. Acknowledgments
  8. Proof for Theorem 1
  9. Bounds on Local Strategies for Parallel Repetitions of KV
  10. k-Repetitions of KV
  11. Preliminaries
  12. Proof of Perfect Parallel Repetition for KV
  13. Proof for Theorem 4

Key Result

Theorem 1

Consider a behavior $P(\bm a|\bm x)$ and a network extension game $\rm{G}^\Gamma$ of the bipartite game $\rm{G}$ given the network graph $\Gamma$. If the score $S^\Gamma$ Eq. eq:networkscore for this behavior fulfills ${S}^\Gamma > {{S}^{\otimes c}_L}$---where $c$ is the capacity of the min-cut of t

Figures (2)

  • Figure 1: Structure of the state for GMNL superactivation. In each round of state preparation in the network, a shared random variable $\lambda = i$ determines the preparation of the state $\sigma_i = \rho_{A_iB_i}\bigotimes_{j\neq i}\ketbra{dd}_{A_jB_j}$. This state consists of a bipartite entangled state shared between Alice $\mathcal{A}$ and the $i$-th Bob $\mathcal{B}_i$, while the remaining Bobs receive a locally orthogonal flag state $|dd\rangle$ shared with Alice.
  • Figure 2: Network-extension game ${\rm G}^\Gamma$ of a bipartite Bell game $\rm G$. All pairs of parties $\mathcal{A}_i\mathcal{A}_j$ connected by the network graph $\Gamma_{ij}=1$ (blue) play the bipartite game $G_{e}$, with $e=\{i,j\}$, receiving inputs and providing outputs (shown in pink, yellow, purple and green). The $G_e$ of all bipartite games are multiplied to get the winning condition of the global game ${G}^\Gamma=\prod_{e\in E} G_e$.

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4