Distilling Entanglement From Random Cascades With Partial "Which Path" Ambiguity

We develop a framework to calculate the density matrix of a pair of photons emitted in a decay cascade with partial "which path" ambiguity. We describe an appropriate entanglement distillation scheme which works also for certain random cascades. The qualitative features of the distilled entanglement are presented in a two dimensional "phase diagram." The theory is applied to the quantum tomography of the decay cascade of a biexciton in a semiconductor quantum dot. Agreement with experiment is obtained.