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.

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

References in corpus (4)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Two-qubit mixed states more entangled than pure states: Comparison of the relative entropy of entanglement for a given nonlocality
• Visualizing Two Qubits
• Beyond the standard entropic inequalities: stronger scalar separability criteria and their applications

Cited by in corpus (8)

• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements
• Maximal Steered Coherence Protection by Quantum Reservoir Engineering
• Effect of Local Channels on Quantum Steering Ellipsoids
• Geometric representation of two-qubit entanglement witnesses
• Trade-off relations of l_1-norm coherence for multipartite systems
• Distribution of spin correlation strengths in multipartite systems