  It is known from Bell's theorem that quantum predictions for some entangled
states cannot be mimicked using local hidden variable (LHV) models. From a
computer science perspective, LHV models may be interpreted as classical
computers operating on a potentially infinite number of correlated bits
originating from a common source. As such, Bell inequality violations achieved
through entangled states are able to characterise the quantum advantage of
certain tasks, so long as the task itself imposes no restriction on the
availability of correlated bits. However, if the number of shared bits is
limited, additional constraints are placed on the possible LHV models and
separable, i.e. disentangled, states may become a useful resource. Bell
violations are therefore no longer necessary to achieve a quantum advantage.
Here we show that in particular, separable states may improve the so-called
random access codes, which is a class of communication problems where one party
tries to read a portion of the data held by another distant party in presence
of finite shared randomness and limited classical communication. We also show
how the bias of classical bits can be used to avoid wrong answers in order to
achieve the optimal classical protocol and how the advantage of quantum
protocols is linked to quantum discord.
