# Table 1 Detection probability of each detector. r and t are the reflectivity and transmissivity of the beam splitter BS, respectively.

$${{\boldsymbol{a}}}_{{\boldsymbol{j}}}^{({\boldsymbol{i}})}\ne {{\boldsymbol{b}}}_{{\boldsymbol{j}}}^{({\boldsymbol{i}})}$$$${{\boldsymbol{a}}}_{{\boldsymbol{j}}}^{({\boldsymbol{i}})}={{\boldsymbol{b}}}_{{\boldsymbol{j}}}^{({\boldsymbol{i}})}$$
$${\beta }_{0j}^{(i)}\mathrm{=1}$$1r2
$${\beta }_{1j}^{(i)}\mathrm{=1}$$0rt
$${\alpha }_{j}^{(i)}\mathrm{=1}$$0t