Multipartite Bound Entangled States that Violate Bell’s Inequality

2001/07/09 by Wolfgang Dür, W. Dür
Computer Science · Mathematics · Physics and Astronomy · #Bell state #Bell's theorem #Hidden variable theory #Mathematical analysis #Mathematics #Multipartite #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Squashed entanglement #Upper and lower bounds #quant-ph

paper · pdf · doi:10.1103/physrevlett.87.230402

published as Phys. Rev. Lett. 87, 230402 (2001) · 4 pages, no figures

arxiv created 2001/07/09 · openalex publication_date 2001/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the relation between distillability of multipartite states and violation of Bell's inequality. We prove that there exist multipartite bound entangled states (i.e., nonseparable, nondistillable states) that violate a multipartite Bell inequality. This implies that (i) violation of Bell's inequality is not a sufficient condition for distillability and (ii) some bound entangled states cannot be described by a local hidden variable model.

Citations

• Bell inequalities and the separability criterion
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Bound Entanglement Can Be Activated
• Separability Criterion for Density Matrices
• Classification of multiqubit mixed states: Separability and distillability properties
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
• On the Einstein Podolsky Rosen paradox