 
Summary: Visualizing two qubits
J. E. Avron, G. Bisker,a
and O. Kenneth
Department of Physics, Technion, 32000 Haifa, Israel
Received 19 July 2007; accepted 17 September 2007; published online 19 October 2007
The notions of entanglement witnesses and separable and entangled states for a two
qubit 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 nonelementary result of Horodecki
et al. Phys. Lett. A 223, 18 1996 that for two qubits, Peres PPT positive
partial transpose test for separability 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 Horodecki et al. Phys.
Lett. A 200, 340344 1995 , which optimizes the violation of the CHSH Bell
inequality. Finally, we give numerical evidence that, remarkably, allowing Alice
and Bob to use three rather than two measurements each does not help them to
distinguish any new entangled SLOCC equivalence class beyond the CHSH
class. © 2007 American Institute of Physics. DOI: 10.1063/1.2795217
I. INTRODUCTION
The world of two qubits is the simplest setting where the notions of entanglement,13,4,16
