Table S2.

Main sources of uncertainty in reconstructing the density matrix of the two-photon state, indicating the resulting maximum systematic error in the concurrence estimate

Variable	Source	Maximum relative uncertainty, %	Maximum concurrence uncertainty
Quantum efficiency	Fiber coupling, detector efficiency, frequency filter transmission	15	0.01
Control polarization	Atom number fluctuation, atom loss	4	0.007
Signal reference phase estimation	Reference fast phase fluctuation, shot noise	5	0.009
Signal power fluctuation	Fiber optics, shot noise	4	0.002
Signal fringe normalization	Power fluctuation, shot noise	5	0.005
Total error	All of the above		0.016

The total systematic error should be compared with the statistical error of 0.005.