Ann↦pmrandom access code (RAC) is an encoding ofnbits intombits such that any initial bit can be recovered with probability at leastp, while in a quantum RAC (QRAC), thenbits are encoded intomqubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access code, or simply EARAC) or recovering multiple bits instead of one. In this paper we generalize the idea of RACs to recovering the value of a given Boolean functionfon any subset of fixed size of the initial bits, which we callf-random access codes. We study and give protocols forf-random access codes with classical (f-RAC) and quantum (f-QRAC) encoding, together with many different resources, e.g. private or shared randomness, shared entanglement (f-EARAC) and Popescu-Rohrlich boxes (f-PRRAC). The success probability of our protocols is characterized by thenoise stabilityof the Boolean functionf. Moreover, we give anupper boundon the success probability of anyf-QRAC with shared randomness that matches its success probability up to a multiplicative constant (andf-RACs by extension), meaning that quantum protocols can only achieve a limited advantage over their classical counterparts.
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