Einstein-Podolsky-Rosen steering and the steering ellipsoid

Abstract

The question of which two-qubit states are steerable (i.e. permit a demonstration of EPR-steering) remains open. Here, a strong necessary condition is obtained for the steerability of two-qubit states having maximally-mixed reduced states, via the construction of local hidden state models. It is conjectured that this condition is in fact sufficient. Two provably sufficient conditions are also obtained, via asymmetric EPR-steering inequalities. Our work uses ideas from the quantum steering ellipsoid formalism, and explicitly evaluates the integral of $\mathbf{n}/({\mathbf{n}}^{⊺}A\mathbf{n}{)}^2$ over arbitrary unit hemispheres for any positive matrix $A$.

To appear in Special Issue of JOSA B on EPR-steering. Minor revisions to v1, new references [18] and [24] added, 11 pages, 1 figure

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Cited by in corpus (75)

• Quantum Steering
• Quantum steering: a review with focus on semidefinite programming
• Self-testing of quantum systems: a review
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
• Demonstration of MultiSetting One-Way Einstein-Podolsky-Rosen Steering in Two-Qubit Systems
• Quantum discord and steering in top quarks at the LHC
• Analog of the Clauser-Horne-Shimony-Holt inequality for steering
• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
• General method for constructing local-hidden-variable models for entangled quantum states
• Algorithmic construction of local hidden variable models for entangled quantum states
• Genuinely multipartite entangled quantum states with fully local hidden variable models and hidden multipartite nonlocality
• Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes
• Quantum information and CP measurement in $H\to {\tau }^{+}{\tau }^{-}$ at future lepton colliders
• Steering Bell-diagonal states
• Entanglement without hidden nonlocality
• Experimental validation of quantum steering ellipsoids and tests of volume monogamy relations
• Volume monogamy of quantum steering ellipsoids for multi-qubit systems
• Most incompatible measurements for robust steering tests
• Experimental Simultaneous Learning of Multiple Non-Classical Correlations
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
• The geometry of the Einstein--Podolsky--Rosen correlations
• Measurement-device-independent entanglement and randomness estimation in quantum networks
• Super-Activation of Quantum Steering
• Non-separability and steerability of two-qubit states from the geometry of steering outcomes
• Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements
• Shareability of Quantum Steering and its Relation with Entanglement
• Covariance Bell inequalities
• Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail to do so
• Reliable experimental certification of one-way Einstein-Podolsky-Rosen steering
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Quantum steering with positive operator valued measures
• Necessary Condition for Steerability of Arbitrary Two-Qubit States with Loss
• Geometric Steering Criterion for Two-qubit States
• Canonical forms of two-qubit states under local operations
• Single-copy activation of Bell nonlocality via broadcasting of quantum states
• Quantum Theory and Local Hidden Variable Theory: General Features and Tests for EPR Steering
• Operational characterization of quantumness of unsteerable bipartite states
• Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
• Shareability of steering in 2-producible states
• Experimental verification of the steering ellipsoid zoo via two-qubit states
• Quantum steering of Bell-diagonal states with generalized measurements
• Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality
• Necessary conditions for steerability of two qubits, from consideration of local operations
• On the pure state outcomes of Einstein-Podolsky-Rosen steering
• Weak measurement effect on optimal estimation with lower and upper bound on relativistic metrology
• Quantum cloning of steering
• Local-hidden-state models for Bell diagonal states and beyond
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Measuring network quantum steerability utilizing artificial neural networks
• Geometric Local Hidden State Model for Some Two-qubit States
• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios
• Keyring models: an approach to steerability
• Characterization of the quantumness of unsteerable tripartite correlations
• Locality of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Role of maximally entangled states in the context of linear steering inequalities
• Analysis of Quantum Steering Measures
• Distribution of spin correlation strengths in multipartite systems
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Environmental effects on nonlocal correlations
• Averaged fidelity-based steering criteria
• Several Trade off Features of Quantum Steering in Distributed Scenario
• Persistency of Genuine Correlations Under Particle Loss
• Hidden Steering Nonlocality in Quantum Networks
• Experimental characterization of the hierarchy of quantum correlations in top quark pairs
• Role of Steering Inequality In Quantum Key Distribution Protocol
• Local-hidden-state models for T-states using finite shared randomness
• From top quarks to enhanced quantum key distribution: A Framework for Optimal Predictability of Quantum Observables
• Preparation of quantum correlations assisted by a steering Maxwell demon
• Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection
• Cyclic Einstein-Podolsky-Rosen Steering
• Protection of quantum steering ellipsoids in non-Markovian environments
• Conditional steering under von-Neumann scenario
• Necessary and sufficient criterion of steering for two-qubit T states