Quantum discord for two-qubit $X$-states: A comprehensive approach inspired by classical polarization optics

Understand

Classical correlation and quantum discord are computed for two-qubit $X$-states.

• Our approach, which is inspired by the methods of classical polarization optics, is geometric in the sense that the entire analysis is tied to the correlation ellipsoid of all normalized conditional states of the A-qubit with measurement elements applied to the B-qubit.
• Aspects of the computation which depend on the location of the reduced state of A inside the ellipsoid get clearly separated from those which do not.
• Our treatment is comprehensive\,: all known results are reproduced, often more economically, and several new insights and results emerge.