Minimal Example of Quantum Nonclassicality without Freedom of Choice.

Area of Science:

• Quantum Information Science
• Causal Inference
• Foundations of Physics

Background:

• Bell's theorem quantifies quantum nonclassicality.
• Generalizing Bell's theorem to causal networks reveals new insights.
• Understanding the simplest quantum nonclassicality is a fundamental question.

Purpose of the Study:

• To identify the simplest scenario exhibiting quantum nonclassicality within causal networks.
• To explore the incompatibility between quantum correlations and classical causality.
• To investigate the role of interventions in enhancing noise robustness for experimental feasibility.

Main Methods:

• Utilizing an entanglement swapping network with three dichotomic variables.
• Analyzing quantum correlations without assuming locality or fixed measurement choices.
• Applying causal inference principles, specifically interventions, to assess noise robustness.

Main Results:

• Demonstrated quantum nonclassicality in a minimal three-variable entanglement swapping network.
• Showcased incompatibility between quantum correlations and classical causality in this simplified setup.
• Confirmed that interventions significantly enhance the noise robustness of the observed nonclassical behavior.

Conclusions:

• The simplest quantum nonclassicality arises from a three-variable entanglement swapping network.
• This network provides a novel framework for studying quantum nonclassicality and its conflict with classical causality.
• Interventions offer a practical pathway for experimentally verifying these quantum phenomena with current technology.