Experimentally Feasible Quantum-Key-Distribution Scheme Using Qubit-Like Qudits And Its Comparison With Existing Qubit- and Qudit-Based Protocols

TL;DR

This paper presents a modified qudit-based quantum key distribution protocol that increases raw key generation per qudit, proves its security, and compares its performance with existing protocols, showing equivalence to the six-state scheme for n=2.

Contribution

The paper introduces a modification to Chau's qudit QKD scheme that enables n bits per qudit, enhancing key rate and security analysis, and compares it with existing protocols.

Findings

The modified protocol can generate n bits of raw key per qudit in noiseless conditions.

Security of the modified protocol is unconditionally proven.

For n=2, the secret key rate matches that of the six-state scheme.

Abstract

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.