Table 1.

Probabilities of single detection ${\mu }_{p|m}$ and coincidence ${\mu }_{pq|m}$ conditioned on the number of photon pairs m.

Term	Expression
${\mu }_{i|m}$	$1-{\mu }_{\overline{i}|m}$
${\mu }_{\overline{i}|m}$	${(1-2\eta {\mathrm{\Gamma }}_i+{\eta }^2{\mathrm{\Gamma }}_{ii})}^m$
${\mu }_{ij|m}$	$1-{\mu }_{\overline{i}|m}-{\mu }_{\overline{j}|m}+{\mu }_{\overline{i}\overline{j}|m}$
${\mu }_{i\overline{j}|m}$	${\mu }_{\overline{j}|m}-{\mu }_{\overline{i}\overline{j}|m}$
${\mu }_{\overline{i}\overline{j}|m}$	${(1-2\eta ({\mathrm{\Gamma }}_i+{\mathrm{\Gamma }}_j)+{\eta }^2({\mathrm{\Gamma }}_{ii}+{\mathrm{\Gamma }}_{jj}+2{\mathrm{\Gamma }}_{ij}))}^m$

Γ_pq is the joint probability distribution, Γ_p is the marginal, and η is the detection quantum efficiency. Barred subscript indicates no detection.