  Random access codes are a type of communication task that is widely used in
quantum information science. The optimal average success probability that can
be achieved through classical strategies is known for any random access code.
However, only a few cases are solved exactly for quantum random access codes.
In this paper, we provide bounds for the fully general setting of n independent
variables, each selected from a d-dimensional classical alphabet and encoded in
a D-dimensional quantum system subject to an arbitrary quantum measurement. The
bound recovers the exactly known special cases, and we demonstrate numerically
that even though the bound is not tight overall, it can still yield a good
approximation.
