Recently, Chau [Phys. Rev. A 92, 062324 (2015)] 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 $\left(\right|i\rangle \pm |j\rangle )/\sqrt{2}$ 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 nondegenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.

• Received 14 March 2016

DOI:https://doi.org/10.1103/PhysRevA.95.022311