Do all pure entangled states violate Bell's inequalities for correlation functions?

2001/10/31 by Marek Zukowski, Marek Żukowski, Časlav Brukner +5 · 6 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physrevlett.88.210402

published as Phys. Rev. Lett. 88 (2002) 210402 · 4 pages, journal version

openalex publication_date 2002/05/09 · arxiv created 2002/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.

Citations

• On the Einstein Podolsky Rosen paradox

Cited by

• Gisin’s Theorem for Arbitrary Dimensional Multipartite States
• Tight correlation-function Bell inequality for multipartited-dimensional systems
• Bell’s Theorem for GeneralN-Qubit States
• Two-setting Bell inequalities for many qubits
• Characterizing quantum correlations in the nonsignaling framework
• Gisin's Theorem for Three Qubits
• Partial separability and entanglement criteria for multiqubit quantum states