Quantum measurement incompatibility does not imply Bell nonlocality

2017/07/31 by Flavien Hirsch, Marco Túlio Quintino, Nicolas Brunner · 79 citations
Arts and Humanities · Computer Science · Mathematics · Physics and Astronomy · #Alice and Bob #Bell state #Bell test experiments #Bell's theorem #Bipartite graph #Connection (principal bundle) #Discrete mathematics #Kochen–Specker theorem #Local hidden variable theory #Mathematics #Operator (biology) #Philosophy and History of Science #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum correlation #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum nonlocality #quant-ph

paper · pdf · open access · doi:10.1103/physreva.97.012129

published in Physical Review A 97(1) (American Physical Society) · See also arXiv:1705.10069 for a related work Small changes on the main text. Some typos were fixed

openalex publication_date 2018/01/25 · arxiv created 2018/02/01 · arxiv updated 2018/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we explicitly present a given set of non-jointly-measurable positive-operator-value measures (POVMs) M_A with the following property. Considering a bipartite Bell test where Alice uses M_A, then for any possible shared entangled state \ensuremathρ and any set of (possibly infinitely many) POVMs N_B performed by Bob, the resulting statistics admits a local model and can thus never violate any Bell inequality. This shows that quantum measurement incompatibility does not imply Bell nonlocality in general.

Citations

• Measurement incompatibility does not give rise to Bell violation in general
• The Quantum Theory of Measurement
• Classical randomness in quantum measurements
• Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
• On the Einstein Podolsky Rosen paradox
• Separability of mixed states: necessary and sufficient conditions
• Convex separation from convex optimization for large-scale problems
• Bell nonlocality

Cited by

• Quantum incompatibility of a physical context
• Joint measurability of quantum effects and the matrix diamond
• Quantum measurement incompatibility in subspaces
• More nonlocality with less entanglement in Clauser-Horne-Shimony-Holt experiments using inefficient detectors