2018/10/31 by Peter J. Brown, Sammy Ragy, Roger Colbeck
Computer Science · Physics and Astronomy · #Cryptographic protocol #Entropy (arrow of time) #Protocol (science) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum cryptography #Qubit #Randomness #Randomness tests #Semidefinite programming #quant-ph
paper · pdf · doi:10.1109/tit.2019.2960252
published as IEEE Transactions on Information Theory 66, 2964-2987 (2020) · 26 (+9) pages, 6 (+1) figures. v2: New result included (Fig. 7) and several updates made based on referee comments
arxiv created 2019/09/25 · openalex publication_date 2019/12/17 · openalex created_date 2019/12/26 · arxiv updated 2020/06/08 · openalex updated_date 2026/08/05
A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security. A large amount of work to date has focussed on a particular protocol based on spot-checking devices using the CHSH inequality. Here we show how to derive randomness expansion rates for a wide range of protocols, with security against a quantum adversary. Our technique uses semidefinite programming and a recent improvement of the entropy accumulation theorem. To support the work and facilitate its use, we provide code that can generate lower bounds on the amount of randomness that can be output based on the measured quantities in the protocol. As an application, we give a protocol that robustly generates up to two bits of randomness per entangled qubit pair, which is twice that established in existing analyses of the spot-checking CHSH protocol in the low noise regime.