The quantum random access code (QRAC) is an important type of quantum communication
protocol, which is especially useful when there is restrictions to the size
of the message that Alice can send Bob. For instance, if Alice wishes to communicate
a string x = x0x1, where x0 and x1 2 f0, . . . , d 􀀀 1g, using the random access
code protocol, it has been shown in previous works that a quantum encodingdecoding
scheme, based on mutually unbiased bases, leads to a higher probability
of Bob correctly guessing either of Alice’s original dits when compared to a classical
encoding-decoding scheme, for any value d of the dit dimension. In this work we
investigated how the performance of the QRAC changes when the communication
is performed through noisy quantum channels. For this purpose, we explored the
Markovian time evolution of a single qudit system by considering the d-dimensional
generalization of five noisy quantum channels: dit flip , d-phase flip, depolarizing,
amplitude damping, and dephasing. We showed that all of these channels can significantly
decrease the QRAC performance. We attempted to counteract the effects
of noise by optimizing this protocol using semidefinite programming. We mitigated
the negative impacts of noise through this technique for the dit flip, d-phase flip and
dephasing channels.