Free randomness can be amplified

By Roger Colbeck, Renato Renner. Nature Physics, 2011

358 citations recorded by the source corpus.

Bell’s equations enable scientists to test the fundamental implications of quantum physics. A central tenet of this idea is that the choice of measurement is truly random. Researchers now show that some Bell experiments can even increase randomness in cases where choice is not entirely free. The concept could increase the usefulness of weakly random sources for more thorough tests of quantum mechanics. Are there fundamentally random processes in nature? Theoretical predictions, confirmed experimentally, such as the violation of Bell inequalities1, point to an affirmative answer. However, these results are based on the assumption that measurement settings can be chosen freely at random2, so assume the existence of perfectly free random processes from the outset. Here we consider a scenario in which this assumption is weakened and show that partially free random bits can be amplified to make arbitrarily free ones. More precisely, given a source of random bits whose correlation with other variables is below a certain threshold, we propose a procedure for generating fresh random bits that are virtually uncorrelated with all other variables. We also conjecture that such procedures exist for any non-trivial threshold. Our result is based solely on the no-signalling principle, which is necessary for the existence of free randomness.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, History and Philosophy of Science

View Paper: https://www.semanticscholar.org/paper/accceae19cef9a740bce78a797fc6529fa9779ad

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Citations in the corpus

Quantum random number generators (2016, background): “A remarkable contribution to quantum randomness amplification is the randomness amplification protocol of (Colbeck and Renner, 2012), which shows there are deterministic protocols that can amplify the randomness in Santha-Vazirani sources using ancillary physical systems.”
Advances in quantum cryptography (2019, neutral): “[719] where the task was introduced.”
Quantum random number generation (2015, methodology): “The ﬁrst randomness ampliﬁcation protocol was proposed by Colbeck and Renner 73 .”