# decoherence free subspace of a single photon

Take the state vector for a single photon as

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

$H, V, \omega$ are the horizontal polarization, vertical polarization and frequency components of the photon. We have a nice, big tensor product space of states for this photon. In particular, we have entangled single photon states! The entanglement of the single photon comes from entangling the polarization with its own frequency. Is it possible to use this effect to create decoherence free subspaces that would be useful in transmitting information within the polarization state of single photons?

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Basically what you are looking at is to find whether there are entangled states in this family that are fixed points of the decoherence operator (or at least nearly so). To know what will happen you therefore need to know what decoherence operator you expect to act here. – SMeznaric Oct 11 '12 at 12:48
I am thinking of fiber optic spans. The most likely cause of decoherence is second order polarization mode dispersion. There are no treatments of this subject in terms of a joint frequency and polarization linear operator. If you know of one, that would help. Generally, frequency is taken as a classical variable. – Ben Sprott Oct 11 '12 at 14:35
Do you know the Kraus operators of the second order polarization mode dispersion when you take frequency as a classical variable? – SMeznaric Oct 11 '12 at 15:59