Key rate of quantum key distribution with hashed two-way classical communication

We propose an information reconciliation protocol that uses two-way classical communication. The key rates of quantum key distribution (QKD) protocols that use our protocol are higher than those using previously known protocols for a wide range of error rates for the Bennett-Brassard 1984 and six-state protocols. We also clarify the relation between the proposed and known QKD protocols, and the relation between the proposed protocol and entanglement distillation protocols.

Figure 1

(Color online) Comparison of the key rates of the six-state protocols. “Proposed” is the key rate of the six-state protocol that uses the proposed IR protocol. “Vollbrecht et al.” is the key rate of the two-way six-state protocol of [18, 25]. “$B$ step” is the key rate of the two-way six-state protocol of [16]. “One way” is the key rate of the one-way six-state protocol with noisy preprocessing [14]. It should be noted that the key rates of two-way six-state protocols of [15, 16, 17] are slightly higher than that of the proposed protocol for error rates higher than about 15%. For error rates higher than 15%, the best protocol among known protocols is the protocol presented by Renner [15], which involves the advantage distillation and the noisy preprocessing proposed by Renner et al. [13, 14].

Figure 2

(Color online) Comparison of the key rates of the BB84 protocols. “Proposed” is the key rate of the BB84 protocol that uses the proposed IR protocol. “Vollbrecht et al.” is the key rate of the two-way BB84 protocol of [18, 25]. “$B$ step” is the key rate of the two-way BB84 protocol of [16]. “One way” is the key rate of the one-way BB84 protocol with noisy preprocessing [14].