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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 function<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>on any subset of fixed size of the initial bits, which we call<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>-random access codes. We study and give protocols for<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>-random access codes with classical (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>-RAC) and quantum (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>-QRAC) encoding, together with many different resources, e.g. private or shared randomness, shared entanglement (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>-EARAC) and Popescu-Rohrlich boxes (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>-PRRAC). The success probability of our protocols is characterized by the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">noise stability<\/mml:mtext><\/mml:mrow><\/mml:math>of the Boolean function<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>. Moreover, we give an<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">upper bound<\/mml:mtext><\/mml:mrow><\/mml:math>on the success probability of any<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>-QRAC with shared randomness that matches its success probability up to a multiplicative constant (and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>-RACs by extension), meaning that quantum protocols can only achieve a limited advantage over their classical counterparts.<\/jats:p>","DOI":"10.22331\/q-2021-03-07-402","type":"journal-article","created":{"date-parts":[[2021,3,7]],"date-time":"2021-03-07T13:09:47Z","timestamp":1615122587000},"page":"402","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":13,"title":["Quantum Random Access Codes for Boolean Functions"],"prefix":"10.22331","volume":"5","author":[{"given":"Jo\u00e3o F.","family":"Doriguello","sequence":"first","affiliation":[{"name":"Quantum Engineering Centre for Doctoral Training, University of Bristol, United Kingdom"},{"name":"School of Mathematics, University of Bristol, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashley","family":"Montanaro","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol, United Kingdom"},{"name":"Phasecraft Ltd."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2021,3,7]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"S. 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