Theory of Computing
-------------------
Title     : Two-Source Extractors Secure Against Quantum Adversaries
Authors   : Roy Kasher and Julia Kempe
Volume    : 8
Number    : 21
Pages     : 461-486
URL       : https://theoryofcomputing.org/articles/v008a021

Abstract
--------

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
Chor-Goldreich (1988) two-source inner product extractor and its
multi-bit variant by Dodis et al. (RANDOM'04).  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.