Unveiling quantum steering by quantum-classical uncertainty complementarity

TL;DR

This paper introduces a new quantum-classical uncertainty complementarity relation that enhances the detection of quantum steering, provides a full entanglement measure for pure states, and experimentally validates these findings using photonic systems.

Contribution

It proposes a tighter complementarity relation between coherence and entropy, leading to a more efficient steering witness and establishing a quantitative link between coherence and steering resources.

Findings

The new steering witness outperforms the entropic uncertainty relation.

The witness acts as a full entanglement measure for pure bipartite states.

Experimental validation confirms the theoretical predictions.

Abstract

One of the remarkable aspects of quantum steering is its ability to violate local uncertainty complementarity relations. In this vein of study, various steering witnesses have been developed. Here, we introduce a novel complementarity relation between system's quantum and classical uncertainties corresponding to the distillable coherence and the von-Neumann entropy, respectively. We show that the proposed complementarity relation is tighter than the entropic uncertainty relation (EUR). Leveraging this result, we propose a steering witness that is more efficient than the EUR. From the operational perspective, the steering witness quantifies the amount of extra distillable coherence facilitated by quantum steerability. Notably, the proposed steering witness serves as a full entanglement measure for pure bipartite states--an ability that the EUR lacks. We also experimentally validate such a property through a photonic system. Furthermore, a deeper connection to the uncertainty principle is revealed by showcasing the steering-induced distillable coherence can quantifies measurement incompatibility and quantum steerability under genuine incoherent operations. Our work establishes a clear quantitative and operational link between coherence and steering, which are vital resources of quantum technologies, and underscores our efforts in bridging the uncertainty principle with quantum coherence.