Geometric representation of two-qubit entanglement witnesses

Abstract

Any two-qubit state can be represented geometrically by a steering ellipsoid inside the Bloch sphere. We extend this approach to represent any block positive two-qubit operator $B$. We derive a novel classification scheme based on the positivity of $\det B$ and $\det B^{{\mathrm{T}}_{\mathrm{B}}}$; this shows that any ellipsoid inside the Bloch sphere must represent either a two-qubit state or a two-qubit entanglement witness. We focus on such witnesses and their corresponding ellipsoids, finding that properties such as witness optimality are naturally manifest in this geometric representation.

arXiv comment8 pages, 4 figures. Published version

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Cited by in corpus (9)

• Quantum coherence of steered states
• Extracting quantum coherence via steering
• Non-separability and steerability of two-qubit states from the geometry of steering outcomes
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• The hierarchies of "witnesses" and the properties and characterization of entangled states as super entanglement witnesses
• On the pure state outcomes of Einstein-Podolsky-Rosen steering
• Entangled states in the role of witnesses
• Weak measurement effect on optimal estimation with lower and upper bound on relativistic metrology
• Witnessing random unitary and projective quantum channels: Complementarity between separable and maximally entangled states