Simple and general bounds on quantum random access codes
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, and there are no known analytical bounds that can be applied in general. In this paper, we provide such a bound for the fully general setting of 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 known special cases, and we demonstrate numerically that even though the bound is not tight overall, it can still yield a good approximation.