Entangled photons – The entangled quantum state |Omega>

The entangled photons leave the BBO crystal, due to the special crystal structure, somewhere along the upper (R) and lower (L) green cone. R and L stand for two orthogonal polarisation directions.
Depending upon the incidence angle of the laser beam to the BBO crystal and other optical components in the beam path, various different polarisations of the photon pairs can be generated. In this experiment, instead of linear polarised photons, circular polarised photons are used.

Each photon pair leaves the crystal somewhere along these two cones. The photons are detected at exactly opposite positions, with circular polarisation (R: clockwise/L: anti-clockwise).

Something quite special occurs at the two points where the cones intersect: It cannot be distinguished whether photon L is found at the left-hand intersection, and photon R at the right-hand intersection of the two cones, or vice versa. Both possibilities are in superposition in the quantum dimension leading to the entangled photon pair Omega.
The detectors Alice and Bob are positioned in such a way that they can measure entangled photon pairs.
Only on the red lines, a superposition and thus entangled photons are created. Only a minute fraction of the photons that hit the BBO crystal lead to such entangled photon pairs. The vast majority of ultraviolet photons pass through the crystal without interaction – see the blue line.
Of the photon pairs that have emerged, in turn, almost all are not entangled but just product states, as they do not leave the crystal at the intersection lines of the two cones – compare the green circles. Only at the intersection of the two cones, the states LR and RL are indistinguishable and thus in superposition, resulting in the emergence of the entangled photon pair Omega.