Unbounded violation of quantum steering inequalities

Abstract

We construct steering inequalities which exhibit unbounded violation. The concept was to exploit the relationship between steering violation and uncertainty relation. To this end we apply mutually unbiased bases and anti-commuting observables, known to exibit the strongest uncertainty. In both cases, we are able to procure unbounded violations. Our approach is much more constructive and transparent than the operator space theory approach employed to obtain large violation of Bell inequalities. Importantly, using anti-commuting observables we are able to obtain a {\it dichotomic} steering inequality with unbounded violation. So far there is no analogous result for Bell inequalities. Interestingly, both the dichotomic inequality and one of our inequalities can not be directly obtained from existing uncertainty relations, which strongly suggest the existence of an unknown kind of uncertainty relation.

References in corpus (6)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• The uncertainty principle determines the non-locality of quantum mechanics
• Grothendieck's constant and local models for noisy entangled quantum states
• Higher entropic uncertainty relations for anti-commuting observables
• Joint measurability, steering and entropic uncertainty

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• Quantum steering: a review with focus on semidefinite programming
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• Gaussian quantum steering and its asymmetry in curved spacetime
• Most incompatible measurements for robust steering tests
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• Retrieving High-Dimensional Quantum Steering From a Noisy Environment with N Measurement Settings
• Steering maps and their application to dimension-bounded steering
• Non-separability and steerability of two-qubit states from the geometry of steering outcomes
• Quantum steering inequality with tolerance for measurement-setting-errors: experimentally feasible signature of unbounded violation
• Resource-efficient high-dimensional entanglement detection via symmetric projections
• Mutual Unbiasedness in Coarse-grained Continuous Variables
• Quantum steering with imprecise measurements
• Classical communication cost of quantum steering
• Satellite-based quantum steering under the influence of spacetime curvature of the Earth
• Certification of incompatible measurements using quantum steering
• EPR Steering inequalities with Communication Assistance
• Complete hierarchy for high-dimensional steering certification
• Monogamy of Einstein-Podolsky-Rosen steering in the background of an asymptotically flat black hole
• Necessary Condition for Steerability of Arbitrary Two-Qubit States with Loss
• Scalable entanglement certification via quantum communication
• Quantum steering for continuous variable in de Sitter space
• Distrustful quantum steering
• Semidefinite relaxations for high-dimensional entanglement in the steering scenario
• Steering and correlations for the single qudit state on the example of $j=3/2$
• The Schmidt rank for the commuting operator framework
• Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
• Detecting the genuine multipartite two-way steerability with linear steering inequalities
• Maximal violation of steering inequalities and the matrix cube
• Averaged fidelity-based steering criteria
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Steering in spin tomographic probability representation
• Violation of steering inequality for generalized equiangular measurements
• Operator space approach to steering inequality
• Experimental simulation of quantum temporal steering beyond rotating-wave approximation
• Random and free observables saturate the Tsirelson bound for CHSH inequality
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• Multipartite steering verification with imprecise measurements