Chained Bell Inequality Experiment with High-Efficiency Measurements

Area of Science:

• Quantum Information Science
• Quantum Foundations
• Atomic Ion Trapping

Background:

• Local realism, a cornerstone of classical physics, posits that physical properties are definite and independent of measurement.
• Bell inequalities provide a mathematical framework to experimentally test local realism against quantum mechanics' predictions.
• Previous experiments have shown violations of Bell inequalities, but often relied on assumptions like fair sampling.

Purpose of the Study:

• To experimentally test local realism by measuring correlations between two ^{9}Be^{+} ions.
• To develop a statistical framework to quantify local-realistic fractions without common assumptions.
• To provide a device-independent certification of entangled Bell states.

Main Methods:

• Performed correlation measurements on two individually trapped ^{9}Be^{+} ions.
• Utilized a chained Bell inequality designed to be sensitive to local-realistic theories.
• Developed and applied a statistical framework to analyze the observed correlations, quantifying the allowable local-realistic fraction.

Main Results:

• Observed correlations that violate the chained Bell inequality, ruling out local-realistic explanations.
• Established a stringent upper bound of 0.327 (at 95% confidence) for the local-realistic fraction of the observed distribution.
• This bound is significantly lower than previously achieved limits, demonstrating a stronger violation of local realism.

Conclusions:

• The experiment provides strong evidence against local-realistic theories in the context of quantum correlations.
• The developed statistical framework offers a robust method for analyzing quantum correlations without relying on potentially invalid assumptions.
• The results offer a device-independent certification of the created Bell states, confirming their non-classical nature.