Quantitative and Optimal Device-Independent Lower Bounds on Detection Efficiency
Oral-In-person
Abstract
Our work 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.
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.
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Presenters
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Arkaprabha Ghosal
- University of New Orleans