Practical randomness amplification and privatisation with implementations on quantum computers

Cameron Foreman1,2, Sherilyn Wright1, Alec Edgington3, Mario Berta4,5, and Florian J. Curchod3

1Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom
2Department of Computer Science, University College London, London, United Kingdom
3Quantinuum, Terrington House, 13–15 Hills Road, Cambridge CB2 1NL, United Kingdom
4Institute for Quantum Information, RWTH Aachen University, Aachen, Germany
5Department of Computing, Imperial College London, United Kingdom

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We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private numbers, even if using an uncharacterised quantum device potentially built by an adversary. Our generation rates are linear in the repetition rate of the quantum device and the classical randomness post-processing has quasi-linear complexity – making it efficient on a standard personal laptop. The statistical analysis is also tailored for real-world quantum devices.
Our protocol is then showcased on several different quantum computers. Although not purposely built for the task, we show that quantum computers can run faithful Bell tests by adding minimal assumptions. In this semi-device-independent manner, our protocol generates (near-)perfectly unbiased and private random numbers on today's quantum computers.

Near-perfect randomness is required for the security of most cryptographic applications. Although essential, a flawless random number generator is extremely hard to build in practice. The main reasons for this are unavoidable hardware imperfections and requiring initial near-perfect randomness to generate more, leading to a circularity. Device-independent randomness amplification and privatisation (DIRAP) protocols solve both issues at the same time. Indeed, DIRAP generates (near-)perfect private randomness from imperfect and non-private randomness, and security claims are made with minimal hardware assumptions, making it well justified in practice. The drawback of DIRAP is that it is notoriously hard to implement.

For the first time, we develop a complete DIRAP protocol, including post-processing in the form of efficient randomness extractors algorithms. To showcase its practicality, we implement our protocol on existing quantum computers. Although this implies making a few additional hardware assumptions, we show these are well justified on certain devices; this is known as “semi-device independence”. In this manner, we use today’s quantum computers to generate randomness for cryptography with the benefits of DIRAP.

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