Self-testing tilted strategies for maximal loophole-free nonlocality
arXiv:2405.08743 · doi:10.1038/s41534-025-01029-6
Abstract
The degree of experimentally attainable nonlocality, as gauged by the loophole-free or effective violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the doubly-tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. We utilize a Jordan's lemma and Gröbner basis-based proof technique to analytically derive self-testing statements for the entire family of doubly-tilted CHSH inequalities and numerically demonstrate their robustness. These results enable us to reveal the insufficiency of even high levels of the Navascués--Pironio--Acín hierarchy to saturate the maximum quantum violation of these inequalities.
Final version, close to published
References in corpus (28)
- Bell nonlocality
- Device-independent security of quantum cryptography against collective attacks
- No Signalling and Quantum Key Distribution
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Device-independent quantum key distribution secure against collective attacks
- Bounding the set of quantum correlations
- Self-testing of quantum systems: a review
- Randomness vs Non Locality and Entanglement
- Closing the detection loophole in Bell experiments using qudits
- Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
- Robust and versatile black-box certification of quantum devices
- Physical characterization of quantum devices from nonlocal correlations
- Non locality, closing the detection loophole and communication complexity
- Detection Loophole in Bell experiments: How post-selected local correlations can look non-local
- Violation of local realism vs detection efficiency
- Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols
- Extremal quantum correlations for N parties with two dichotomic observables per site
- Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables
- Bell Inequalities From No-Signalling Distributions
- Exponentially decreasing critical detection efficiency for any Bell inequality
- Bell nonlocality with a single shot
- An elegant proof of self-testing for multipartite Bell inequalities
- Minimum detection efficiency for a loophole-free violation of the Braunstein-Caves chained Bell inequalities
- Graph-theoretic approach to Bell experiments with low detection efficiency
- Certifying long-range quantum correlations through routed Bell tests
- Revisited aspects of the local set in CHSH Bell scenario
- Joint-measurability and quantum communication with untrusted devices
- Introducing Moment: A toolkit for semi-definite programming with moment matrices