Time and frequency as quantum continuous variables

We present a second quantization description of frequency-based continuous variables quantum computation in the subspace single photons. For this, we define frequency and time operators using free-field Hamiltonian its Fourier transform, show that these observables, when restricted to one photon per mode subspace, reproduce canonical position-momentum commutation relations. As consequence, can be used universal set gates this particular subspace. discuss physical implementation as well their effect on states, also implement information protocols, same way than polarization is currently two-dimensional variable.