Institute for Quantum Information (IQI) Weekly Seminar

Randomness extractors are an important building block for classical and quantum cryptography. They are used for privacy amplification which is an essential step in quantum key distribution but also in many other protocols such as device independent randomness amplification and expansion. For most of these applications, it is important that the extractor be quantum-proof, i.e., be secure against quantum adversaries. It is known that some extractor constructions are quantum-proof whereas others are provably not. We argue that the theory of operator spaces offers a natural framework for studying to what extent extractors are secure in the presence of quantum adversaries.

In this talk, I will start by formulating the definition of extractors as a condition on the norm of an associated operator. Then, after introducing the basics of the theory of operator spaces, I will show that the definition of quantum-proof extractors can be formulated as a condition on the completely bounded norm of the same operator. As an application, we use Grothendieck's inequality to show that very high min-entropy extractors are always approximately quantum-proof.

This is joint work with Mario Berta and Volkher Scholz. Quantum-proof extractors via operator space theory