Experimentally ruling out joint reality based on operational completeness

TL;DR

This study experimentally demonstrates that joint reality of two observables on a qubit is incompatible with operational completeness, using a device-independent approach and inequality violations on a trapped ion system.

Contribution

It provides the first device-independent experimental test of the incompatibility between joint reality and operational completeness for a single qubit.

Findings

Violation of inequalities confirms incompatibility.

Nonlinear criteria are more noise-robust.

Results advance understanding of quantum-classical boundary.

Abstract

Whether the observables of a physical system admit real values is of fundamental importance to a deep understanding of nature. In this work, we report a device-independent experiment to confirm that the joint reality of two observables on a single two-level system is incompatible with the assumption of operational completeness, which is strictly weaker than that of preparation noncontextuality. We implement two observables on a trapped $^{171}{\rm Yb}^{+}$ ion to test this incompatibility via violation of certain inequalities derived from both linear and nonlinear criteria. Moreover, by introducing a highly controllable dephasing channel, we show that the nonlinear criterion is more robust against noise. Our results push the fundamental limit to delineate the quantum-classical boundary and pave the way for exploring relevant problems in other scenarios.