  We prove the unconditional security of the six-state protocol with threshold
detectors and one-way classical communication. Unlike the four-state protocol
(BB84), it has been proven that the squash operator for the six-state does not
exist, i.e., the statistics of the measurements cannot be obtained via
measurement on qubits. We propose a technique to determine which photon number
states are important, and we consider a fictitious measurement on a qubit,
which is defined through the squash operator of BB84, for the better estimation
of Eve's information. As a result, we prove that the bit error rate threshold
for the six-state protocol (12.611%) remains almost the same as the one of the
qubit-based six-state protocol (12.619%). This clearly demonstrates the
robustness of the six-state protocol against the use of the practical devices.
