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.