Two-Source Extractors Secure against Quantum Adversaries

We initiate the study of multi-source extractors in the quantum world. In this setting, our goal is to extract random bits from two independent weak random sources, on which two quantum adversaries store a bounded amount of information. Our main result is a two-source extractor secure against quantum adversaries, with parameters closely matching the classical case and tight in several instances. Moreover, the extractor is secure even if the adversaries share entanglement. The construction is the ChorGoldreich [CG88] two-source inner product extractor and its multi-bit variant by Dodis et al. [DEOR04]. Previously, research in this area focused on the construction of seeded extractors secure against quantum adversaries; the multi-source setting poses new challenges, among which is the presence of entanglement that could potentially break the independence of the sources. ∗Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel. Supported by JK’s Individual Research Grant of the Israeli Science Foundation. †Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel. Supported by the European Commission under the Integrated Project Qubit Applications (QAP) funded by the IST directorate as Contract Number 015848, by an Alon Fellowship of the Israeli Higher Council of Academic Research, by an Individual Research Grant of the Israeli Science Foundation, by a European Research Council (ERC) Starting Grant, by a Raymond and Beverly Sackler Career Development Chair and by the Wolfson Family Charitable Trust.