Quantitative and Optimal Device-Independent Lower Bounds on Detection Efficiency

Fuente: arXiv
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Main Authors: Ghosal, Arkaprabha, Patra, Soumyadip, Bierhorst, Peter
Format: Preprint
Published: 2025
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author Ghosal, Arkaprabha
Patra, Soumyadip
Bierhorst, Peter
author_facet Ghosal, Arkaprabha
Patra, Soumyadip
Bierhorst, Peter
contents This paper examines a quantitative and optimal lower bound on the detector efficiency in a (2,2,2) Bell experiment within a fully device-independent framework, whereby the detectors used in the experiment are uncharacterized. We provide a tight lower bound on the minimum efficiency required to observe a desired Bell-CHSH violation using the Navascués-Pironio-Acín (NPA) hierarchy, confirming tightness up to four decimal places with numerical optimization over explicit quantum realizations. We then introduce the effect of dark counts and demonstrate how to quantify the minimum required efficiency to observe a desired CHSH violation with an increasing dark count error. Finally, to obtain an analytical closed-form expression of the minimum efficiency, we consider the set of no-signaling behaviors that satisfy the Tsirelson bound, which are easier to characterize than the quantum set. Using such behaviors, we find a simple closed-form expression for a lower bound on the minimum efficiency which is monotonically increasing with the CHSH violation, though the analytically obtained lower bounds are meaningfully below the numerically tight lower bound.
format Preprint
id arxiv_https___arxiv_org_abs_2511_19302
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantitative and Optimal Device-Independent Lower Bounds on Detection Efficiency
Ghosal, Arkaprabha
Patra, Soumyadip
Bierhorst, Peter
Quantum Physics
This paper examines a quantitative and optimal lower bound on the detector efficiency in a (2,2,2) Bell experiment within a fully device-independent framework, whereby the detectors used in the experiment are uncharacterized. We provide a tight lower bound on the minimum efficiency required to observe a desired Bell-CHSH violation using the Navascués-Pironio-Acín (NPA) hierarchy, confirming tightness up to four decimal places with numerical optimization over explicit quantum realizations. We then introduce the effect of dark counts and demonstrate how to quantify the minimum required efficiency to observe a desired CHSH violation with an increasing dark count error. Finally, to obtain an analytical closed-form expression of the minimum efficiency, we consider the set of no-signaling behaviors that satisfy the Tsirelson bound, which are easier to characterize than the quantum set. Using such behaviors, we find a simple closed-form expression for a lower bound on the minimum efficiency which is monotonically increasing with the CHSH violation, though the analytically obtained lower bounds are meaningfully below the numerically tight lower bound.
title Quantitative and Optimal Device-Independent Lower Bounds on Detection Efficiency
topic Quantum Physics
url https://arxiv.org/abs/2511.19302