  In a deterministic quantum key distribution (DQKD) protocol with a two-way
quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the
qubit and sends it back to Bob. After measuring the returned qubit, Bob can
obtain Alice's key bit immediately, without basis reconciliation. Since an
eavesdropper may attack the qubits traveling on either the Bob-Alice channel or
the Alice-Bob channel, the security analysis of DQKD with a two-way quantum
channel is complicated and its unconditional security has been controversial.
This paper presents a security proof of a single-photon four-state DQKD against
general attacks.
