The Measurement Equation for a Generic Interferometer

$\displaystyle \vec{V}_{\rm ij}^{}$ =	$\displaystyle \left[\vphantom{{{G}_i\otimes{G}^_j}}\right.$ G_i $\displaystyle \otimes$ G^_j $\displaystyle \left.\vphantom{{{G}_i\otimes{G}^_j}}\right]$ $\displaystyle \left[\vphantom{{{D}_i\otimes{D}^_j}}\right.$ D_i $\displaystyle \otimes$ D^_j $\displaystyle \left.\vphantom{{{D}_i\otimes{D}^_j}}\right]$ $\displaystyle \left[\vphantom{{{C}_i\otimes{C}^_j}}\right.$ C_i $\displaystyle \otimes$ C^_j $\displaystyle \left.\vphantom{{{C}_i\otimes{C}^*_j}}\right]$
	$\displaystyle \sum_{k}^{}$ $\displaystyle \left[\vphantom{{{E}_i {\left(\underline{\rho}_k\right)} \otimes {E}^_j{\left(\underline{\rho}_k\right)}}}\right.$ E_i $\displaystyle \left(\vphantom{\underline{\rho}_k}\right.$ $\displaystyle \underline{\rho}_{k}^{}$ $\displaystyle \left.\vphantom{\underline{\rho}_k}\right)$ $\displaystyle \otimes$ E^_j $\displaystyle \left(\vphantom{\underline{\rho}_k}\right.$ $\displaystyle \underline{\rho}_{k}^{}$ $\displaystyle \left.\vphantom{\underline{\rho}_k}\right)$ $\displaystyle \left.\vphantom{{{E}_i {\left(\underline{\rho}_k\right)} \otimes {E}^_j{\left(\underline{\rho}_k\right)}}}\right]$ $\displaystyle \left[\vphantom{{{P}_i {\left(\underline{\rho}_k\right)} \otimes {P}^_j{\left(\underline{\rho}_k\right)}}}\right.$ P_i $\displaystyle \left(\vphantom{\underline{\rho}_k}\right.$ $\displaystyle \underline{\rho}_{k}^{}$ $\displaystyle \left.\vphantom{\underline{\rho}_k}\right)$ $\displaystyle \otimes$ P^_j $\displaystyle \left(\vphantom{\underline{\rho}_k}\right.$ $\displaystyle \underline{\rho}_{k}^{}$ $\displaystyle \left.\vphantom{\underline{\rho}_k}\right)$ $\displaystyle \left.\vphantom{{{P}_i {\left(\underline{\rho}_k\right)} \otimes {P}^_j{\left(\underline{\rho}_k\right)}}}\right]$ $\displaystyle \left[\vphantom{{{F}_i {\left(\underline{\rho}_k\right)} \otimes {F}^_j{\left(\underline{\rho}_k\right)}}}\right.$ F_i $\displaystyle \left(\vphantom{\underline{\rho}_k}\right.$ $\displaystyle \underline{\rho}_{k}^{}$ $\displaystyle \left.\vphantom{\underline{\rho}_k}\right)$ $\displaystyle \otimes$ F^_j $\displaystyle \left(\vphantom{\underline{\rho}_k}\right.$ $\displaystyle \underline{\rho}_{k}^{}$ $\displaystyle \left.\vphantom{\underline{\rho}_k}\right)$ $\displaystyle \left.\vphantom{{{F}_i {\left(\underline{\rho}_k\right)} \otimes {F}^*_j{\left(\underline{\rho}_k\right)}}}\right]$
	S $\displaystyle \vec{\cal I}_{k}^{}$ e^-2i-	(1)