  Most qubit-based quantum key distribution (QKD) protocols extract the secure
key merely from single-photon component of the attenuated lasers. However, with
the Scarani-Acin-Ribordy-Gisin 2004 (SARG04) QKD protocol, the unconditionally
secure key can be extracted from the two-photon component by modifying the
classical post-processing procedure in the BB84 protocol. Employing the merits
of SARG04 QKD protocol and six-state preparation, one can extract secure key
from the components of single photon up to four photons. In this paper, we
provide the exact relations between the secure key rate and the bit error rate
in a six-state SARG04 protocol with single-photon, two-photon, three-photon,
and four-photon sources. By restricting the mutual information between the
phase error and bit error, we obtain a higher secure bit error rate threshold
of the multiphoton components than previous works. Besides, we compare the
performances of the six-state SARG04 with other prepare-and-measure QKD
protocols using decoy states.
