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Free randomness can be amplified

Nature Physics volume 8, pages 450–453 (2012)Cite this article

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Abstract

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.

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Figure 1: Illustration of the bipartite set-up.
Figure 2: Typical causal structure of a protocol.

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Acknowledgements

We thank V. Galliard for useful discussions and L. del Rio for the figures. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. R.R. acknowledges support from the Swiss National Science Foundation (grant No 200020-135048, the National Centre of Competence in Research QSIT and the CHIST-ERA project DIQIP) and from the European Research Council (grant No 258932).

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Authors and Affiliations

  1. Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

    Roger Colbeck & Renato Renner

  2. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada

    Roger Colbeck

Authors
  1. Roger Colbeck
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  2. Renato Renner
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Both authors contributed equally to this work.

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Correspondence to Roger Colbeck.

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The authors declare no competing financial interests.

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Colbeck, R., Renner, R. Free randomness can be amplified. Nature Phys 8, 450–453 (2012). https://doi.org/10.1038/nphys2300

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