Detectability of Post-Quantum Correlations in Symmetry-Restricted Bell Scenarios
Abstract
Searches for post-quantum correlations depend on two distinct ingredients: how abundant such correlations are in the underlying correlation space and how efficiently the chosen representation preserves their distinguishability from quantum correlations. We quantify these effects by introducing the popularity rate and the projection acceptance, whose product defines the search performance. We apply these concepts in binary-outcome Bell scenarios with symmetry-related sites, using the CHSH and pyramid representations. Particular attention is paid to the distinction between exchange-symmetric synchronous correlations and correlations satisfying only exchange symmetry. In the synchronous quantum sector, the common-vector representation follows automatically from synchrony, whereas exchange symmetry alone defines a substantially larger correlation space. We show that this distinction can qualitatively change the effectiveness of a projected search: the pyramid representation, which retains substantial discriminatory power in the synchronous sector, has no discriminatory power when only exchange symmetry is imposed. Our results provide a simple framework for assessing and comparing searches for post-quantum correlations.
Related
- tt̅ spin correlations from toponium production scenarios to non-relativistic resummation beyond the standard perturbative baseline
- Quantum Gibbs sampling through the detectability lemma
- Strong Symmetry from Two-Point Correlations
- Symmetry-resolved fermionic correlations in iron-oxide ground spaces
- Provably Efficient Learning of Fermionic Correlations under Particle-Number Symmetry
BibTeX
@misc{gazdzicki2026detectability,
title = {{Detectability of Post-Quantum Correlations in Symmetry-Restricted Bell Scenarios}},
author = {Marek Gazdzicki and Francesco Giacosa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.15705},
eprint = {2609.15705},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15705},
}
RIS
TY - UNPB
TI - Detectability of Post-Quantum Correlations in Symmetry-Restricted Bell Scenarios
AU - Marek Gazdzicki
AU - Francesco Giacosa
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2609.15705
UR - https://arxiv.org/abs/2609.15705
AB - Searches for post-quantum correlations depend on two distinct ingredients: how abundant such correlations are in the underlying correlation space and how efficiently the chosen representation preserves their distinguishability from quantum correlations. We quantify these effects by introducing the popularity rate and the projection acceptance, whose product defines the search performance. We apply these concepts in binary-outcome Bell scenarios with symmetry-related sites, using the CHSH and pyramid representations. Particular attention is paid to the distinction between exchange-symmetric synchronous correlations and correlations satisfying only exchange symmetry. In the synchronous quantum sector, the common-vector representation follows automatically from synchrony, whereas exchange symmetry alone defines a substantially larger correlation space. We show that this distinction can qualitatively change the effectiveness of a projected search: the pyramid representation, which retains substantial discriminatory power in the synchronous sector, has no discriminatory power when only exchange symmetry is imposed. Our results provide a simple framework for assessing and comparing searches for post-quantum correlations.
ER -