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

Separable states improve protocols with restricted randomness