Figure 5: Optical implementation of different causal relations.

(a) Schematic diagram of the experiment. The gate allows the implementation of different ways of combining a common-cause relation (between C and B) with a cause-effect relation (between D and B). The initial preparation targets the maximally entangled state . One photon is measured at C and reprepared at D; then both are sent through the gate. The photon at B is detected in coincidence with the photon at F to post select only on those cases wherein a pair was produced. (b) Experimental set-up, including the polarization-entangled photon source and the partial swap, which implements the unitary by tilting the glass plates to a specific angle in the Sagnac interferometer. (i) For the quantum mixtures, no dephasing is applied and a translation stage adjusts the delay of the photon at E with respect to the one at D. (ii) For the classical mixtures, the LCRs and wave plates are used to apply complete dephasing on D, E and B, respectively. Notation for optical elements: bismuth-borate (BiBO), β-barium-borate (BBO), half-wave plate (HWP), quarter-wave plate (QWP), liquid-crystal retarder (LCR), polarizing beam splitter (PBS), non-polarizing beam splitter (NPBS), avalanche photo diode (APD).