This paper introduces a novel approach to quantum steering by establishing a complementarity relation between quantum and classical uncertainties in quantum systems. The authors develop a quantum-classical uncertainty complementarity relation (QCUR) that links distillable coherence with von Neumann entropy, proving this relation is tighter than traditional entropic uncertainty relations (EUR).
The research demonstrates that QCUR serves as a more efficient steering witness than previous approaches, with significant operational meaning: it quantifies the additional distillable coherence enabled by quantum steerability. Unlike previous steering witnesses, this new approach works for arbitrary dimensions without requiring full-state tomography, making it more practical for real-world applications.
A remarkable property of the QCUR-based steering witness is its ability to function as a complete entanglement measure for pure bipartite states—a capability lacking in previous approaches including EUR, complementarity relations for mutually unbiased bases, and Reid’s criteria. The authors validate this property through photonic system experiments.
The paper further establishes connections between quantum steering and measurement incompatibility, showing that QCUR violations can quantify measurement incompatibility. This reveals deeper relationships between the generalized uncertainty principle and quantum steering. The authors also explore the asymmetric nature of their steering witness, its ability to detect one-way steering, and its monotonic behavior.
By establishing quantitative and operational links between coherence and steering—both crucial resources for quantum technologies—this work bridges fundamental quantum principles with practical applications. It demonstrates how the interplay between quantum and classical uncertainties can be harnessed to better detect and quantify quantum correlations, potentially advancing quantum information processing technologies including random number generation, key distribution, metrology, and thermodynamics.
Reference: Lee, KY., Lin, JD., Lemr, K. et al. Unveiling quantum steering by quantum-classical uncertainty complementarity. npj Quantum Inf 11, 72 (2025). doi:10.1038/s41534-025-01017-w
