Bounding the Set of Quantum Correlations

2006/07/31 by Miguel Navascués, Miguel Navascues, Stefano Pironio +2 · 2 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physrevlett.98.010401

published as Phys. Rev. Lett. 98, 010401 (2007) · 5 pages, no figures. v2: minor modifications

openalex publication_date 2007/01/04 · arxiv created 2008/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We introduce a hierarchy of conditions necessarily satisfied by any distribution P_alphabeta representing the probabilities for two separate observers to obtain outcomes alpha and beta when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Among other applications, our approach can be used to obtain upper bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the violations of the Collins et al. inequalities.

Citations

• Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
• Empirical two-point correlation functions
• Quantum non-locality in two three-level systems
• Semidefinite Programming

Cited by

• Cryptography in a Quantum World
• Bell nonlocality