# fiber optic second order PMD as an operator on the tensor product Hilbert space

Second order polarization mode dispersion (SOPMD) is a coupling mechanism between polarization and frequency. Take our photon to be the following tensor product:

$\psi = \int \gamma_{\omega} | \omega \rangle \otimes (\alpha |H \rangle + \beta | V \rangle )d \omega$

then, can we model SOPMD as an entangling operator, $O_{SO}$, on this joint space? Furthermore, can we model certain kinds of noise in fibre transmission systems as this operator, $O_{SO}$, followed by the tracing out of one or both of polarization or frequency?

$\rho^{\prime} = Tr_{Pol} (O_{SO} \rho O_{SO}^{\dagger})$

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