Device-independent quantum key distribution based on measurement inputs

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Abstract
We provide an analysis of a family of device-independent quantum key distribution (QKD) protocols that has the following features. (a) The bits used for the secret key do not come from the results of the measurements on an entangled state but from the choices of settings. (b) Instead of a single security parameter (a violation of some Bell inequality) a set of them is used to estimate the level of trust in the secrecy of the key. The main advantage of these protocols is a smaller vulnerability to imperfect random number generators made possible by feature (a). We prove the security and the robustness of such protocols. We show that using our method it is possible to construct a QKD protocol which retains its security even if the source of randomness used by communicating parties is strongly biased. As a proof of principle, an explicit example of a protocol based on the Hardy's paradox is presented. Moreover, in the noiseless case, the protocol is secure in a natural way against any type of memory attack, and thus allows one to reuse the device in subsequent rounds. We also analyze the robustness of the protocol using semidefinite programming methods. Finally, we present a postprocessing method, and observe a paradoxical property that rejecting some random part of the private data can increase the key rate of the protocol.
Funding Information
  • Fundacja na rzecz Nauki Polskiej (TEAM/2011-8/9/styp7)
  • European Research Council (291348)
  • Narodowe Centrum Nauki (2013/08/M/ST2/00626, DEC-2011/02/A/ST2/00305)
  • Ministerstwo Nauki i Szkolnictwa Wyższego (IdP2011 000361)
  • University Grants Commission

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