H. F. Chau

H. F. Chau, Qinan Wang, Cardythy Wong

Recently, Chau introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a $2^n$-dimensional Hilbert space in the form $(|i\rangle\pm|j\rangle)/\sqrt{2}$ with $n\ge 2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate $n$ bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional $(n-1)$ bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of $n=2$, the secret key rate of this modified protocol using non-degenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.

H. F. Chau, C. -H. Fred Fung, H. -K. Lo

Bit commitment (BC) is an important cryptographic primitive for an agent to convince a mutually mistrustful party that she has already made a binding choice of 0 or 1 but only to reveal her choice at a later time. Ideally, a BC protocol should be simple, reliable, easy to implement using existing technologies, and most importantly unconditionally secure in the sense that its security is based on an information-theoretic proof rather than computational complexity assumption or the existence of a trustworthy arbitrator. Here we report such a provably secure scheme involving only one-way classical communications whose unconditional security is based on no superluminal signaling (NSS). Our scheme is inspired by the earlier works by Kent, who proposed two impractical relativistic protocols whose unconditional securities are yet to be established as well as several provably unconditionally secure protocols which rely on both quantum mechanics and NSS. Our scheme is conceptually simple and shows for the first time that quantum communication is not needed to achieve unconditional security for BC. Moreover, with purely classical communications, our scheme is practical and easy to implement with existing telecom technologies. This completes the cycle of study of unconditionally secure bit commitment based on known physical laws.