Unveiling quantum steering by quantum-classical uncertainty complementarity
arXiv:2312.01055 · doi:10.1038/s41534-025-01017-w
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.
20 pages, 5 figures
References in corpus (60)
- Quantum entanglement
- Quantifying Coherence
- Bell nonlocality
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Operational Resource Theory of Coherence
- The Uncertainty Principle in the Presence of Quantum Memory
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- Entropic Uncertainty Relations and their Applications
- The Einstein-Podolsky-Rosen paradox: from concepts to applications
- Quantum Steering
- Observable measure of quantum coherence in finite dimensional systems
- Characterizing Nonclassical Correlations via Local Quantum Uncertainty
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Quantum steering: a review with focus on semidefinite programming
- Entropic uncertainty relations - A survey
- Quantifying Einstein-Podolsky-Rosen steering
- One-way Einstein-Podolsky-Rosen Steering
- Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
- Assisted distillation of quantum coherence
- All Entangled Quantum States Are Nonlocal
- Joint measurability of generalized measurements implies classicality
- Quantum root-mean-square error and measurement uncertainty relations
- Kochen-Specker Contextuality
- One-to-one mapping between steering and joint measurability problems
- Quantum inference of states and processes
- Non-Local Advantage of Quantum Coherence
- Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
- All sets of incompatible measurements give an advantage in quantum state discrimination
- One-shot coherence distillation
- Incompatible measurements in quantum information science
- Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
- Maximal randomness expansion from steering inequality violations using qudits
- Probabilistic distillation of quantum coherence
- A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
- Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox
- Nonlocal advantage of quantum coherence in high-dimensional states
- Quantum uncertainty relation using coherence
- Wave-particle duality: an information-based approach
- Quantum and classical entropic uncertainty relations
- Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
- Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits
- Temporal steering and security of quantum key distribution with mutually-unbiased bases against individual attacks
- Certifying single-system steering for quantum information processing
- Experimental demonstration of measurement-device-independent measure of quantum steering
- One-Shot Coherence Distillation: Towards Completing the Picture
- Quantifying Quantumness of Channels Without Entanglement
- Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
- Non-asymptotic assisted distillation of quantum coherence
- Quantum steerability: characterization, quantification, superactivation and unbounded amplification
- No-signaling Principle Can Determine Optimal Quantum State Discrimination
- Securing quantum networking tasks with multipartite Einstein-Podolsky-Rosen steering
- Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources
- Steering-enhanced quantum metrology using superpositions of noisy phase shifts
- Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication
- Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
- Deep learning the hierarchy of steering measurement settings of qubit-pair states
- Quantum steering as a witness of quantum scrambling
- Asymmetry and tighter uncertainty relations for Rényi entropies via quantum-classical decompositions of resource measures
- Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering
- Thermodynamic Approach to Quantifying Incompatible Instruments