There has in the past been some interest

There has in the past been some interest in using squeezed states of light. The quantum noise limit I have assumed is that of a Glauber coherent state, which saturates the Heisenberg inequality σxσp≥ℏ2 and has equal uncertainty in the conjugate "position" and "momentum" variables.

On a phase plane, this can be translated into a lower bound on the product of amplitude and phase uncertainties. One can produce squeezed states with less phase uncertainty at the expense of amplitude uncertainty,

so the idea was to use a frequency or phase modulated transmission scheme and lower the uncertainty in the transmitted phase. However, one of course gets a worsening of the amplitude SNR (we can't in quantum mechanics, thwart the Heisenberg inequality), so such schemes make marginal if any difference to the overall SNR. They certainly won't change the orders of magnitudes I discussed above.
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Here is an excellent summary paper on the subject, fleshing out my summary above and discussing quantitative modifications to the model above for noises other than the "fundamental" quantum noise (especially Raman and Amplified Spontaneous Emission): René-Jean Essiambre, Gerhard Kramer, Peter J. Winzer, Gerard J. Foschini, and Bernhard Goebel, "Capacity Limits of Optical Fiber Networks", J. LIGHTWAVE TECH., VOL. 28, NO. 4, FEBRUARY 15, 2010.