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.

8 pages, 4 figures. Published version

References in corpus (8)

• Entanglement detection
• Inferring causal structure: a quantum advantage
• Quantum steering ellipsoids, extremal physical states and monogamy
• Structural approximations to positive maps and entanglement breaking channels
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Spectral properties of entanglement witnesses
• Construction of optimal witness for unknown two-qubit entanglement
• Visualizing Two Qubits

Cited by in corpus (1)

• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid