Mutually Unbiased Bases In 3 and 4 Dimensions Semi-quantum Key Distribution Protocol

Semi-quantum key distribution is traditionally based on two-level quantum systems. In this paper, an unconditional security of a semi quantum key distribution protocol based on higher-dimensional systems using various mutually unbiased bases is presented. We first consider the three dimensional case using three and four mutually unbiased bases and derive a lower bound for the key rate as a function of the quantum channel's noise. We then generalize the result to a semi-quantum key distribution protocol that employs different number of mutually unbiased bases for four-dimensional states. It is found that basing the semi-quantum key distribution protocol on higher-dimensional mutually unbiased bases can increase the tolerable threshold of the noise and the maximum achievable value of the secret key rate.