Quantum Cryptography with Weak Measurements

Abstract: In this article we present a new prepare and measure quantum key distribution protocol that decouples the necessary quantum channel error estimation from its dependency on sifting, or otherwise post-selecting, the detection outcomes. Rather than estimating Eve's coupling to the quantum channel from the statistics of the sifted key, we infer this information from weak measurements made equally on all of the received photons immediately prior to post-selection by the photon detectors. We prove that the accuracy of the weak measurement parameter estimation is robust to reasonable device imperfections, even in an adversarial environment, and hence the asymptotic security of this protocol can be inferred from the security analysis of BB84. In addition to eliminating detector basis-dependent attacks, such as detector blinding, we demonstrate that this new prepared and measure QKD protocol is immune to a very powerful class of measurement-side device attacks that also allow an adversary control of the weak measurement outcomes given two modest requirements placed on the measurement-side devices. Finally, we compare the asymptotically achievable secure key rate of a decoy state version of the weak measurement protocol and show it is essentially equal to that of BB84 with decoy states and significantly higher than MDI-QKD for realistic system parameters.