Operational Coherent Measurements with Steering and Randomness

Abstract

Measurement incompatibility underpins randomness generation in nonlocal phenomena. However, at its root, a more fundamental quantum feature is noncommuting (or coherent) measurements. This raises a central question: How can we operationally characterize the quantum advantage of coherent measurements within nonlocal correlations? We answer this by demonstrating that coherent measurements can leverage semi-device-independent (SDI) steering, enabling local randomness generation from any set of coherent measurements. Specifically, we establish that a measurement assemblage can be used to demonstrate SDI steering if and only if it is coherent, providing a complete operational characterization. To quantify this resource, we formulate a nonconvex resource theory for SDI steering and propose an operational monotone for the two-setting scenario by mapping noncommuting measurements to SDI steering. Our framework enables a practical quantum random number generator based on SDI steering that eliminates the need to certify entanglement and tolerates arbitrarily low detection efficiency. That is, we demonstrate that genuine randomness can be generated via coherent measurements beyond standard steerable states and even beyond entangled states under realistic experimental conditions. These results extend the scope of quantum resources for generating nonlocal correlations beyond measurement incompatibility, revealing the operational power of coherent measurements.