The binary-outcome detection loophole

authored by: Thomas Cope
Abstract: The detection loophole problem arises when quantum devices fail to provide an output for some runs. If treating these devices in a device-independent manner, failure to include the unsuccessful runs in the output statistics can lead to an adversary falsifying security i.e. Bell inequality violation. If the devices fail with too high frequency, known as the detection threshold, then no security is possible, as the full statistics cannot violate a Bell inequality. In this work we provide an intuitive local hidden-variable strategy that the devices may use to falsify any two-party, binary-outcome no-signalling distribution up to a threshold of 2(m A + m B - 8)/(m A m B - 16), where m A, m B refer to the number of available inputs choices to the two parties. This value is the largest analytically predicted lower bound for no-signalling distributions. We strongly conjecture it gives the true detection threshold for m A = m B, and for computationally tractable scenarios we provide the Bell inequality which verifies this. We also prove that a non-trivial detection threshold remains, even when allowing one party an arbitrary number of input choices.
Organisation(s): Institute of Theoretical Physics
QuantumFrontiers
Type: Article
Journal: New journal of physics
Volume: 23
ISSN: 1367-2630
Publication date: 22.07.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Physics and Astronomy(all)
Electronic version(s): https://doi.org/10.1088/1367-2630/ac10a5 (Access: Open)

BibTeX

@article{e0610aa2097e4762839b416755233339,
title = "The binary-outcome detection loophole",
abstract = "The detection loophole problem arises when quantum devices fail to provide an output for some runs. If treating these devices in a device-independent manner, failure to include the unsuccessful runs in the output statistics can lead to an adversary falsifying security i.e. Bell inequality violation. If the devices fail with too high frequency, known as the detection threshold, then no security is possible, as the full statistics cannot violate a Bell inequality. In this work we provide an intuitive local hidden-variable strategy that the devices may use to falsify any two-party, binary-outcome no-signalling distribution up to a threshold of 2(m A + m B - 8)/(m A m B - 16), where m A, m B refer to the number of available inputs choices to the two parties. This value is the largest analytically predicted lower bound for no-signalling distributions. We strongly conjecture it gives the true detection threshold for m A = m B, and for computationally tractable scenarios we provide the Bell inequality which verifies this. We also prove that a non-trivial detection threshold remains, even when allowing one party an arbitrary number of input choices.",
keywords = "detection loophole, hidden variables, nonlocal correlations, quantum foundations, quantum information",
author = "Thomas Cope",
note = "This work was supported, in part, by the Quantum Valley Lower Saxony (QVLS), the DFG through SFB 1227 (DQ-mat), the RTG 1991, and funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy-EXC-2123 Quantum Frontiers-390837967. We would like to thank Tobias J Osborne, Reinhard F Werner and Le Phuc Thinh for useful discussions. The publication of this article was funded by the Open Access Fund of the Leibniz Universit{\"a}t Hannover.",
year = "2021",
month = jul,
day = "22",
doi = "10.1088/1367-2630/ac10a5",
language = "English",
volume = "23",
journal = "New journal of physics",
issn = "1367-2630",
publisher = "IOP Publishing Ltd.",
number = "7",
}