Quantum Random Access Codes with Mutually Unbiased Bases in Three-Dimensional Hilbert Space

Quantum random access codes (QRACs) are key tools for a variety of protocols in quantum information theory. This paper gives an upper bound on the guessing success probability in the classical case of random access codes using mutually unbiased bases as measurement bases in a 3-dimensional Hilbert space and gives an encoding strategy capable of exceeding the classical bound. This encoding strategy holds for both 3-1 and 4-1 QRACs. This result is useful in areas such as random number expansion.