Seedless extractors for device-independent quantum cryptography

Device-independent (DI) quantum cryptography aims at providing secure cryptography with minimal trust in, or characterisation of, the underlying quantum devices. A key step in DI protocols is randomness extraction (or privacy amplification), which typically requires a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi></mml:math> of additional bits with sufficient entropy and statistical independence from any bits generated during the protocol. In this work, we propose a method for extraction in DI protocols that does not require a seed and is secure against computationally unbounded quantum adversaries. The core idea is to use the Bell violation of the raw data, rather than its min-entropy, as the extractor promise. We present a complete security proof in a model where the experiment uses memoryless measurement devices acting on an arbitrary joint (across all rounds) state. Our results mark a first step in this alternative, seedless, approach to extraction in DI protocols.