  We address the question of existence of private quantum channel for qubits
encoded in polarization degrees of freedom of a photon, that remains secure
even if multi-photon (instead of single-photon) pulse is emitted. We show that
random unitary channel distributed according to SU(2) Haar measure has this
property. Further we analyze the qubit unitary k-designs. We show they ensure
security if the photons' parity of the source is guaranteed. Otherwise, the
qubit unitary k-designs do not guarantee perfect security.
