Tight steering inequalities from generalized entropic uncertainty relations

Abstract

We establish a general connection between entropic uncertainty relations, Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we construct steering inequalities from any entropic uncertainty relation, given that the latter satisfies two natural properties. We obtain steering inequalities based on Rényi entropies. These turn out to be tight in many scenarios, using max- and min-entropy. Considering steering tests with two noisy measurements, our inequalities exactly recover the noise threshold for steerability. This is the case for any pair of qubit 2-outcome measurements, as well as for pairs of mutually unbiased bases in any dimension. This shows that easy-to-evaluate quantities such as entropy can optimally witness steering, despite the fact that they are coarse-grained representations of the underlying statistics.

References in corpus (26)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• The Uncertainty Principle in the Presence of Quantum Memory
• One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
• On quantum Renyi entropies: a new generalization and some properties
• The operational meaning of min- and max-entropy
• Entropic Uncertainty Relations and their Applications
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• The Uncertainty Relation for Smooth Entropies
• Quantum steering: a review with focus on semidefinite programming
• EPR Steering Inequalities from Entropic Uncertainty Relations
• Conjectured Strong Complementary Information Tradeoff
• Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
• An Invitation to Quantum Incompatibility
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Joint measurability of generalized measurements implies classicality
• Uncertainty relations from simple entropic properties
• One-to-one mapping between steering and joint measurability problems
• Information theoretical properties of Tsallis entropies
• Uncertainty relations for MUBs and SIC-POVMs in terms of generalized entropies
• Quantifying measurement incompatibility of mutually unbiased bases
• Steering criteria from general entropic uncertainty relations
• Informationally complete joint measurements on finite quantum systems
• Multipartite steering inequalities based on entropic uncertainty relations
• Joint measurability, steering and entropic uncertainty
• Generalized conditional entropy in bipartite quantum systems

Cited by in corpus (28)

• Quantum Steering
• Improved tripartite uncertainty relation with quantum memory
• The geometry of the Einstein--Podolsky--Rosen correlations
• Experimental demonstration of robust quantum steering
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• Entropic uncertainty relations from quantum designs
• Entropic uncertainty relations from equiangular tight frames and their applications
• Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states
• Unification of quantum resources in tripartite systems
• Experimental certification of steering criterion based on general entropic uncertainty relation
• Experimental observation the Einstein-Podolsky-Rosen Steering based on the detection of entanglement
• Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
• Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems
• Estimating the Shannon entropy and (un)certainty relations for design-structured POVMs
• Uncertainty relations for quantum measurements from generalized equiangular tight frames
• Entropic uncertainty relations for multiple measurements assigned with biased weights
• Detecting the genuine multipartite two-way steerability with linear steering inequalities
• Analysis of Quantum Steering Measures
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Averaged fidelity-based steering criteria
• Tight bounds from multiple-observable entropic uncertainty relations
• Complementarity relations for design-structured POVMs in terms of generalized entropies of order $\alpha \in (0,2)$
• Better Heisenberg limits, coherence bounds, and energy-time tradeoffs via quantum Rényi information
• Parameterized steering criteria via correlation matrices
• Conditional states and entropy in qudit-qubit systems
• Experimental demonstration of complementarity relations between quantum steering criteria
• Witness High-Dimensional Quantum Steering via Majorization Lattice
• Imprecise quantum steering inequalities in tripartite systems