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We investigate secret key rates for the quantum repeater using encoding [L.Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standardrepeater scheme by Briegel, D\"ur, Cirac, and Zoller. The former scheme has theadvantage of a minimal consumption of classical communication. We analyze thetrade-off in the secret key rate between the communication time and therequired resources. For this purpose, we introduce an error model for therepeater using encoding which allows for input Bell states with a fidelitysmaller than one, in contrast to the model given in [L. Jiang et al., Phys.Rev. A 79, 032325 (2009)]. We show that one can correct additional errors inthe encoded connection procedure of this repeater and develop a suitabledecoding algorithm. Furthermore, we derive the rate of producing entangledpairs for the quantum repeater using encoding and give the minimal parameters(gate quality and initial fidelity) for establishing a nonzero secret key. Wefind that the generic quantum repeater is optimal regarding the secret key rateper memory per second and show that the encoded quantum repeater using thesimple three-qubit repetition code can even have an advantage with respect tothe resources compared to other recent quantum repeater schemes with encoding.

Secret key rates for an encoded quantum repeater