Upper bound on device-independent quantum key distribution with two way classical postprocessing under individual attack

Device-independent quantum key distribution (DI-QKD) can guarantee the security even with untrusted devices. Unfortunately, conventional DI-QKD protocols can tolerate low noises only and require high detection efficiencies to achieve positive key rates. To improve the noise robustness, one promising solution is implementing the two-way classical postprocessing, which has the advantage of reducing the bit errors. In this paper, we study the DI-QKD with B-step two-way classical postprocessing under individual attacks. We adopt the tool of convex combination attack, i.e. an optimal individual attack, to upper bound the Devetak-Winter key rate. We show that, by using the B-step procedure, our protocol can tolerate detection efficiencies as low as $81.0\%$ and depolarising noise of 0.799, which is better than the thresholds for the protocol with one-way error correction. This result can serve as the lower bounds on the critical noise and detection efficiency for the scenarios under general attacks. Our work justifies the advantage of two-way classical postprocessing for DI-QKD, thus offering a step towards its applications.