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

References in corpus (5)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Loopholes in Bell Inequality Tests of Local Realism
• Nonlocality of a single photon: paths to an EPR-steering experiment

Cited by in corpus (18)

• Analog of the Clauser-Horne-Shimony-Holt inequality for steering
• Super-Activation of Quantum Steering
• Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements
• Covariance Bell inequalities
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Shareability of steering in 2-producible states
• Experimental verification of the steering ellipsoid zoo via two-qubit states
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Measuring network quantum steerability utilizing artificial neural networks
• Analysis of Quantum Steering Measures
• Hidden Steering Nonlocality in Quantum Networks
• Distribution of spin correlation strengths in multipartite systems
• Experimental characterization of the hierarchy of quantum correlations in top quark pairs
• From top quarks to enhanced quantum key distribution: A Framework for Optimal Predictability of Quantum Observables
• Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection
• Cyclic Einstein-Podolsky-Rosen Steering
• Necessary and sufficient criterion of steering for two-qubit T states
• Protection of quantum steering ellipsoids in non-Markovian environments