Abstract
We present an asymptotic security proof of deterministic quantum key distribution (DQKD) with a two-way quantum channel. The security proof of DQKD with a two-way quantum channel is different from that of BB84, because Eve can attack the travel qubits twice, both in line Bob to Alice and in line Alice to Bob. With the no-signaling principle and the property of mutual information, we obtain an upper bound of the final key generation of entanglement-based DQKD and hence single-photon four-state DQKD. Our results can be applied to the protocol of QKD with two-step quantum channels.
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