Visualizing Two Qubits

Understand

The notions of entanglement witnesses, separable and entangled states for two qubits system can be visualized in three dimensions using the SLOCC equivalence classes.

• This visualization preserves the duality relations between the various sets and allows us to give ``proof by inspection'' of a non-elementary result of the Horodeckies that for two qubits, Peres separability test is iff.
• We then show that the CHSH Bell inequalities can be visualized as circles and cylinders in the same diagram.
• This allows us to give a geometric proof of yet another result of the Horodeckies, which optimizes the violation of the CHSH Bell inequality.