Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes

Abstract

Fully characterizing the steerability of a quantum state of a bipartite system has remained an open problem since the concept of steerability was defined. In this work, using our recent geometrical approach to steerability, we suggest a necessary and sufficient condition for a two-qubit state to be steerable with respect to projective measurements. To this end, we define the critical radius of local models and show that a state of two qubits is steerable with respect to projective measurements from Alice's side if and only if her critical radius of local models is less than $1$. As an example, we calculate the critical radius of local models for the so-called T-states by proving the optimality of a recently-suggested ansatz for Alice's local hidden state model.

5 pages, 1 figures; comments are very welcome

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• Quantum information and CP measurement in $H\to {\tau }^{+}{\tau }^{-}$ at future lepton colliders
• 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
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
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• Super-Activation of Quantum Steering
• Steerability detection of arbitrary 2-qubit state via machine learning
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
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• Maximal Steered Coherence Protection by Quantum Reservoir Engineering
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• Geometric Steering Criterion for Two-qubit States
• Canonical forms of two-qubit states under local operations
• Experimental verification of the steering ellipsoid zoo via two-qubit states
• Quantum steering of Bell-diagonal states with generalized measurements
• Shareability of steering in 2-producible 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
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• 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
• Measuring network quantum steerability utilizing artificial neural networks
• Experimental Verification of Anisotropic Invariance for Three-Qubit States
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• Analysis of Quantum Steering Measures
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Averaged fidelity-based steering criteria
• Experimental characterization of the hierarchy of quantum correlations in top quark pairs
• Local-hidden-state models for T-states using finite shared randomness
• Protection of quantum steering ellipsoids in non-Markovian environments
• Quantum steerability based on joint measurability
• Quantum correlations in composite systems under global unitary operations
• Preparation of quantum correlations assisted by a steering Maxwell demon
• Conditional steering under von-Neumann scenario