Exact Identification of Quantum Correlations in the Minimal Bell Scenario
Abstract
Bell nonlocality places the long-standing philosophical disputes over the nature of quantum theory on a mathematically rigorous, experimentally testable footing, positioning quantum mechanics between local realism and the most general no-signaling theories. Yet the precise quantum boundary has remained elusive even in the minimal Bell scenario, where the extreme points generating the set are known. Here we characterize this boundary through a computable necessary and sufficient criterion: a correlation is quantum if and only if it can be decomposed into an extreme quantum correlation and a classical correlation. The criterion follows from our proof that every Bell functional exhibiting quantum advantage admits a unique quantum maximizer. We further classify the finitely many maximal-face structures containing each nonlocal exposed point according to their local deterministic vertices. By sharply distinguishing physically realizable correlations from nonphysical ones, these results resolve a long-standing open problem and provide a new foundation for identifying the principles underlying quantum theory and determining the ultimate information-theoretic limits of quantum correlations.
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BibTeX
@misc{sun2026exact,
title = {{Exact Identification of Quantum Correlations in the Minimal Bell Scenario}},
author = {Liang-Liang Sun and Jie Wang and Sixia Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34364},
eprint = {2610.34364},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34364},
note = {CC0},
}
RIS
TY - UNPB
TI - Exact Identification of Quantum Correlations in the Minimal Bell Scenario
AU - Liang-Liang Sun
AU - Jie Wang
AU - Sixia Yu
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34364
UR - https://arxiv.org/abs/2610.34364
AB - Bell nonlocality places the long-standing philosophical disputes over the nature of quantum theory on a mathematically rigorous, experimentally testable footing, positioning quantum mechanics between local realism and the most general no-signaling theories. Yet the precise quantum boundary has remained elusive even in the minimal Bell scenario, where the extreme points generating the set are known. Here we characterize this boundary through a computable necessary and sufficient criterion: a correlation is quantum if and only if it can be decomposed into an extreme quantum correlation and a classical correlation. The criterion follows from our proof that every Bell functional exhibiting quantum advantage admits a unique quantum maximizer. We further classify the finitely many maximal-face structures containing each nonlocal exposed point according to their local deterministic vertices. By sharply distinguishing physically realizable correlations from nonphysical ones, these results resolve a long-standing open problem and provide a new foundation for identifying the principles underlying quantum theory and determining the ultimate information-theoretic limits of quantum correlations.
ER -