Semiquantum key distribution

Secure key distribution between two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? Recently, a semiquantum key distribution protocol was presented [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], in which one of the parties (Bob) is classical, and yet, the protocol is proven to be completely robust against an eavesdropping attempt. Here we extend that result much further. We present two protocols with this constraint and prove their complete robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate parties could notice. One protocol presented here is identical to the one referred to above; however, its robustness is proven here in a much more general scenario. The other protocol is very different as it is based on randomization.

Figure 1

(a) Eve’s maximum (over all attacks) information on the INFO string vs the allowed disturbance on the bits tested by Alice and Bob, in a completely robust (solid line), partly robust (dashed), and completely nonrobust (densely dotted) protocol. (b) Robustness should not be confused with security; Eve’s maximum information on the final key vs allowed disturbance in a secure protocol; such a protocol could be completely or partly robust.

Figure 2

Bit usage summary.