Quantum steering ellipsoids, extremal physical states and monogamy

Abstract

Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the geometric data describe a physical state and investigate maximal volume ellipsoids lying on the physical-unphysical boundary. We derive monogamy relations for steering that are strictly stronger than the Coffman-Kundu-Wootters (CKW) inequality for monogamy of concurrence. The CKW result is thus found to follow from the simple perspective of steering ellipsoid geometry. Remarkably, we can also use steering ellipsoids to derive non-trivial results in classical Euclidean geometry, extending Euler's inequality for the circumradius and inradius of a triangle.

arXiv comment21 pages, 4 figures. Published version with correction given in New J. Phys. 17, 019501 (2015) incorporated

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Cited by in corpus (64)

• Quantum Steering
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• One-to-one mapping between steering and joint measurability problems
• Monogamy of quantum correlations - a review
• Entangled Bloch Spheres: Bloch Matrix and Two Qubit State Space
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• Rigidity of quantum steering and one-sided device-independent verifiable quantum computation
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• Steering Bell-diagonal states
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• Volume monogamy of quantum steering ellipsoids for multi-qubit systems
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• Complementarity Relations Between Quantum Steering Criteria
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering
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• Quantum steering inequality with tolerance for measurement-setting-errors: experimentally feasible signature of unbounded violation
• Maximal Steered Coherence Protection by Quantum Reservoir Engineering
• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
• Conditional Mutual Information and Quantum Steering
• Effect of Local Channels on Quantum Steering Ellipsoids
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Authentication protocol based on collective quantum steering
• Canonical forms of two-qubit states under local operations
• Absolute Non-Violation of a Three-Setting Steering Inequality by Two-Qubit States
• Conclusive Identification of Quantum Channels via Monogamy of Quantum Correlations
• Geometric representation of two-qubit entanglement witnesses
• Nonclassical steering and the Gaussian steering triangoloids
• Operational characterization of quantumness of unsteerable bipartite states
• Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement
• Two-qubit causal structures and the geometry of positive qubit-maps
• Lower bounds on violation of monogamy inequality for quantum correlation measures
• Shareability of steering in 2-producible states
• Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality
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• Simple permutation-based measure of quantum correlations and maximally-3-tangled states
• Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states
• Role of maximally entangled states in the context of linear steering inequalities
• Characterization of the quantumness of unsteerable tripartite correlations
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Several Trade off Features of Quantum Steering in Distributed Scenario
• Distribution of spin correlation strengths in multipartite systems
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• The Euler and Grace-Danielsson inequalities for nested triangles and tetrahedra: a derivation and generalisation using quantum information theory
• Quantum steering ellipsoids and quantum obesity in critical systems
• Conditional states and entropy in qudit-qubit systems
• Swapping of quantum correlations and the role of local filtering operations
• On the notion of quantum copulas
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• Cyclic Einstein-Podolsky-Rosen Steering