Typical Werner states satisfying all linear Bell inequalities with dichotomic measurements

2017/11/10 by Ming-Xing Luo, Ming‐Xing Luo · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Bell state #Bell test experiments #Bell's theorem #CHSH inequality #Combinatorics #Homogeneous #Inequality #Local hidden variable theory #Mathematical analysis #Mathematics #Multipartite #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum channel #Quantum entanglement #Quantum mechanics #Quantum teleportation #State (computer science) #quant-ph

paper · pdf · doi:10.1103/physreva.97.042301

published as Phys. Rev. A 97, 042301, 2018 · 23 pages

arxiv created 2017/11/10 · openalex created_date 2017/11/17 · openalex publication_date 2018/04/03 · arxiv updated 2018/06/26 · openalex updated_date 2026/08/05

Abstract

Quantum entanglement as a special resource inspires various distinct applications in quantum information processing. Unfortunately, it is NP-hard to detect general quantum entanglement using Bell testing. Our goal is to investigate quantum entanglement with white noises that appear frequently in experiment and quantum simulations. Surprisingly, for almost all multipartite generalized Greenberger-Horne-Zeilinger states there are entangled noisy states that satisfy all linear Bell inequalities consisting of full correlations with dichotomic inputs and outputs of each local observer. This result shows generic undetectability of mixed entangled states in contrast to Gisin's theorem of pure bipartite entangled states in terms of Bell nonlocality. We further provide an accessible method to show a nontrivial set of noisy entanglement with small number of parties satisfying all general linear Bell inequalities. These results imply typical incompleteness of special Bell theory in explaining entanglement.

Citations

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