Non-separability and steerability of two-qubit states from the geometry of steering outcomes

Abstract

When two qubits A and B are in an appropriate state, Alice can remotely steer Bob's system B into different ensembles by making different measurements on A. This famous phenomenon is known as quantum steering, or Einstein-Podolsky-Rosen steering. Importantly, quantum steering establishes the correspondence not only between a measurement on A (made by Alice) and an ensemble of B (owned by Bob) but also between each of Alice's measurement outcomes and an unnormalized conditional state of Bob's system. The unnormalized conditional states of B corresponding to all possible measurement outcomes of Alice are called Alice's steering outcomes. We show that, surprisingly, the $4$-dimensional geometry of Alice's steering outcomes completely determines both the non-separability of the two-qubit state and its steerability from her side. Consequently, the problem of classifying two-qubit states into non-separable and steerable classes is equivalent to geometrically classifying certain $4$-dimensional skewed double-cones.

7 pages, 2 figures; improved figures and terminology

References in corpus (9)

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• Geometric representation of two-qubit entanglement witnesses

Cited by in corpus (23)

• Quantum Steering
• Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes
• Volume monogamy of quantum steering ellipsoids for multi-qubit systems
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
• The geometry of the Einstein--Podolsky--Rosen correlations
• Maximal Steered Coherence Protection by Quantum Reservoir Engineering
• Reliable experimental certification of one-way Einstein-Podolsky-Rosen steering
• Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail to do so
• Quantum steering with positive operator valued measures
• Canonical forms of two-qubit states under local operations
• Collision model approach to steering of an open driven qubit
• Shareability of steering in 2-producible states
• Quantum steering of Bell-diagonal states with generalized measurements
• Experimental verification of the steering ellipsoid zoo via two-qubit states
• Necessary conditions for steerability of two qubits, from consideration of local operations
• On the pure state outcomes of Einstein-Podolsky-Rosen steering
• 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
• Keyring models: an approach to steerability
• Cost of Simulating Entanglement in Steering Scenario
• Protection of quantum steering ellipsoids in non-Markovian environments