Negativity and steering: a stronger Peres conjecture

Abstract

The violation of a Bell inequality certifies the presence of entanglement even if neither party trusts their measurement devices. Recently Moroder et. al. showed how to make this statement quantitative, using semidefinite programming to calculate how much entanglement is certified by a given violation. Here I adapt their techniques to the case where Bob's measurement devices are in fact trusted, the setting for "EPR-steering" inequalities. Interestingly, all of the steering inequalities studied turn out to require negativity for their violation. This supports a significant strengthening of Peres' conjecture that negativity is required to violate a bipartite Bell inequality.

5 pages, 3 tables, 2 figures, code at http://www.mattpusey.co.uk/steer

References in corpus (4)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Grothendieck's constant and local models for noisy entangled quantum states

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• One-way Einstein-Podolsky-Rosen Steering
• Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Joint measurability of generalized measurements implies classicality
• One-to-one mapping between steering and joint measurability problems
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• The resource theory of steering
• SuperDense Teleportation using Hyperentangled Photons
• Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems
• Physical characterization of quantum devices from nonlocal correlations
• Optimal randomness certification in the quantum steering and prepare-and-measure scenarios
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
• Quantifying Non-Markovianity with Temporal Steering
• Maximal randomness expansion from steering inequality violations using qudits
• Evaluation of convex roof entanglement measures
• Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
• Steering criteria from general entropic uncertainty relations
• General method for constructing local-hidden-variable models for entangled quantum states
• Rigidity of quantum steering and one-sided device-independent verifiable quantum computation
• Algorithmic construction of local hidden variable models for entangled quantum states
• Verifying the quantumness of a channel with an untrusted device
• Self-testing through EPR-steering
• Universal steering inequalities
• The type-independent resource theory of local operations and shared randomness
• Network Quantum Steering
• Semidefinite programming relaxations for quantum correlations
• Steering Bell-diagonal states
• Unbounded violation of quantum steering inequalities
• Continuous variable steering and incompatibility via state-channel duality
• Demonstration of EPR steering using single-photon path entanglement and displacement-based detection
• Most incompatible measurements for robust steering tests
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• Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• The geometry of the Einstein--Podolsky--Rosen correlations
• Fundamental limits on key rates in device-independent quantum key distribution
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• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• Super-Activation of Quantum Steering
• Characterization of quantum correlations with local dimension constraints and its device-independent applications
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• Steerability detection of arbitrary 2-qubit state via machine learning
• One-sided Device-independent Self-testing of any Pure Two-qubit Entangled State
• Hierarchy in temporal quantum correlations
• Detecting Einstein-Podolsky-Rosen steering through entanglement detection
• Pearson Correlation Coefficient as a measure for Certifying and Quantifying High Dimensional Entanglement
• Spatio-Temporal Steering for Testing Nonclassical Correlations in Quantum Networks
• Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification
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• A family of nonlocal bound entangled states
• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• Classical communication cost of quantum steering
• Experimental demonstration of one-sided device-independent self-testing of any pure two-qubit entangled state
• Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages
• Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
• Post-quantum steering is a stronger-than-quantum resource for information processing
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Characterizing Nonlocal Correlations via Universal Uncertainty Relations
• Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes
• EPR Steering inequalities with Communication Assistance
• Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
• Einstein-Podolsky-Rosen steering based on semi-supervised machine learning
• Detected the steerability bounds of the generalized Werner states via BackPropagation neural network
• Detecting genuine multipartite entanglement in steering scenarios
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• Geometric Steering Criterion for Two-qubit States
• Experimental observation the Einstein-Podolsky-Rosen Steering based on the detection of entanglement
• Quantum measurement incompatibility in subspaces
• One-way Einstein-Podolsky-Rosen steering beyond qubits
• Operational characterization of quantumness of unsteerable bipartite states
• Family of Bell inequalities violated by higher-dimensional bound entangled states
• The resource theory of nonclassicality of channel assemblages
• Superunsteerability as a quantifiable resource for random access codes assisted by Bell-diagonal states
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• Thermodynamic Approach to Quantifying Incompatible Instruments
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• Uniform Quantification of Correlations for Bipartite Systems
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• Necessary conditions for steerability of two qubits, from consideration of local operations
• Zero Uncertainty States in the Presence of Quantum Memory
• Detection of Network and Genuine Network Quantum Steering
• Quantum Resource Control for noisy EPR-steering with qubit measurements
• Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Geometric Local Hidden State Model for Some Two-qubit States
• Adjusting inequalities for detection-loophole-free steering experiments
• Detecting EPR steering via two classes of local measurements
• Measuring network quantum steerability utilizing artificial neural networks
• On characterising assemblages in Einstein-Podolsky-Rosen scenarios
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• Detecting the genuine multipartite two-way steerability with linear steering inequalities
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• Maximal violation of steering inequalities and the matrix cube
• An Effective Way of Characterizing the Quantum Nonlocality
• Detecting Tripartite Steering via Quantum Entanglement
• Postquantum steering
• Certifying quantumness beyond steering and nonlocality and its implications on quantum information processing
• Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states
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• Bell and steering scenarios in terms of operator systems
• Activation of post-quantumness in bipartite generalised EPR scenarios
• Optimal CHSH values for regular polygon theories in generalized probabilistic theories
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• An optimal measurement strategy to beat the quantum uncertainty in correlated system
• Entanglement Cost for Steering Assemblages
• Experimental simulation of quantum temporal steering beyond rotating-wave approximation
• Broadcasting of non-locality
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• A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
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