Not yet reviewed by Pith; the record is open.

In quantum sideband high harmonic generation (QSHHG), high harmonic generation is perturbed by a bright quantum field resulting in harmonic sidebands, with the intent to transfer non-classical properties from the quantum perturbation to the harmonic sidebands. So far, non-classical features have not been found in QSHHG yet. The closed form theory of QSHHG in atoms and solids developed here answers the question under which conditions non-classical features can be realized. QSHHG results in a multi-mode entanglement between harmonic sideband modes and perturbative quantum mode. A projective measurement on either creates a variety of non-classical states commonly used in quantum information science. This opens a pathway towards quantum engineering high harmonic generation as a short wavelength source for quantum information science.