The last layer made one exciton emit one photon. Pump the dot harder and you load two electron–hole pairs — a biexciton. It can't release both at once; it decays in a two-step cascade, emitting two photons in sequence. And when the dot is symmetric enough, those two photons come out polarization-entangled — a single semiconductor crystal acting as an on-demand source of quantum-correlated light.
Real physics: the XX→X→0 radiative cascade, biexciton binding shift, and the fine-structure-splitting condition for entanglement (Benson et al. 2000; demonstrated by Akopian 2006, Stevenson 2006). Idealized model; limits stated at the end.
Two decay routes connect XX to ground — one through each intermediate exciton spin state. If those two states have the same energy (FSS = 0), you can't tell which route the dot took, the routes interfere, and the pair emerges entangled. Open a splitting and the routes become distinguishable — the entanglement washes out into ordinary correlated light.
Loading two excitons gives the biexciton state |XX⟩, sitting near twice the single-exciton energy but shifted by the biexciton binding energy (the two pairs interact). A photon can only carry away one exciton's worth of energy, so the dot decays in steps: |XX⟩ → |X⟩ emits the first photon, then |X⟩ → |0⟩ emits the second. Because the biexciton is shifted, the two photons have slightly different energies — which is exactly how experimentalists tell the cascade photons apart.
The instrument tracks both photon energies live from your binding setting, and judges the two-photon state from the fine-structure splitting — degenerate paths give the entangled Bell-type state, a nonzero splitting collapses it toward classical correlation.
From the biexciton there are two ways down to the ground state: through the horizontally-polarized exciton or the vertically-polarized one. Each path emits its pair with matching polarization — |H,H⟩ on one road, |V,V⟩ on the other. Quantum mechanics says: if nothing in the universe records which road was taken, the dot takes both, and the emitted pair is the superposition (|HH⟩ + |VV⟩)/√2 — a maximally entangled Bell state. The thing that can betray the road is the fine-structure splitting: a tiny energy difference between the two intermediate states, caused by the dot being slightly asymmetric. Make the dot symmetric (FSS → 0) and the roads become identical — entanglement restored.
Two electron–hole pairs. The starting line of the cascade. Bound a few meV from twice the single exciton.
Via the H exciton or the V exciton. Same energy ⇒ indistinguishable ⇒ interference ⇒ entanglement.
Asymmetry splits the two roads in energy, tagging the path and erasing entanglement. The engineering goal is FSS → 0.
Background: O. Benson et al., "Regulated and Entangled Photons from a Single Quantum Dot" (Phys. Rev. Lett., 2000); N. Akopian et al. and R. M. Stevenson et al., experimental entangled-pair emission (2006). Biexciton cascade is standard quantum-dot quantum-optics.