Three dimensional quantum key distribution in the presence of several eavesdroppers

TL;DR

This paper extends quantum key distribution protocols to three-dimensional systems with multiple eavesdroppers, analyzing security scenarios with varying numbers of eavesdroppers and bases, and deriving mutual information expressions.

Contribution

It introduces a three-dimensional QKD protocol with multiple eavesdroppers and analyzes its security and information sharing in various attack scenarios.

Findings

Four-basis protocol is more secure against a single eavesdropper.

Security depends on attack probabilities with multiple eavesdroppers.

Large number of eavesdroppers significantly impacts protocol security.

Abstract

Quantum key distribution based on encoding in three dimensional systems in the presence of several eavesdroppers is proposed. This extends the BB84 protocol in the presence of many eavesdroppers where two-level quantum systems (qubits) are replaced by three-level systems (qutrits). We discuss the scenarios involving two, three and four complementary bases. We derive the explicit form of Alice and Bob mutual information and the information gained by each eavesdropper. In particular, we show that, in the presence of only one eavesdropper, the protocol involving four bases is safer than the other ones. However, for two eavesdroppers, the security is strongly dependent on the attack probabilities. The effect of a large number of eavesdroppers is also investigated.