Quantum-proof randomness extractors via operator space theory

Understand

Quantum-proof randomness extractors are an important building block for classical and quantum cryptography as well as device independent randomness amplification and expansion.

• Furthermore they are also a useful tool in quantum Shannon theory.
• It is known that some extractor constructions are quantum-proof whereas others are provably not [Gavinsky et al., STOC'07].
• We argue that the theory of operator spaces offers a natural framework for studying to what extent extractors are secure against quantum adversaries: we first phrase the definition of extractors as a bounded norm condition between normed spaces, and then show that the presence of quantum adversaries corresponds to a completely bounded norm condition between operator spaces.