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Von Neumann Normalisation and Symptoms of Randomness: An Application to Sequences of Quantum Random Bits

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Book cover Unconventional Computation (UC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6714))

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Abstract

Due to imperfections in measurement and hardware, the flow of bits generated by a quantum random number generator (QRNG) contains bias and correlation, two symptoms of non-randomness. There is no algorithmic method to eliminate correlation as this amounts to guaranteeing incomputability. However, bias can be mitigated: QRNGs use normalisation techniques such as von Neumann’s method—the first and simplest technique for reducing bias—and other more efficient modifications.

In this paper we study von Neumann un-biasing normalisation for an ideal QRNG operating ‘to infinity’, i.e. producing an infinite bit-sequence. We show that, surprisingly, von Neumann un-biasing normalisation can both increase or decrease the (algorithmic) randomness of the generated sequences. The impact this has on the quality of incomputability of sequences of bits from QRNGs is discussed.

A successful application of von Neumann normalisation—in fact, any un-biasing transformation—does exactly what it promises, un-biasing, one (among infinitely many) symptoms of randomness; it will not produce ‘true’ randomness, a mathematically vacuous concept.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Alastair A. Abbott & Cristian S. Calude

Authors
  1. Alastair A. Abbott
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  2. Cristian S. Calude
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Science Centre, The University of Auckland, 38 Princes Street, 1142, Auckland, New Zealand

    Cristian S. Calude

  2. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Jarkko Kari

  3. Department of Information Technologies, Åbo Akademi University, ICT Building, Joukahaisenkatu 3-5 A, 20520, Turku, Finland

    Ion Petre

  4. Leiden Institute of Center Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

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Abbott, A.A., Calude, C.S. (2011). Von Neumann Normalisation and Symptoms of Randomness: An Application to Sequences of Quantum Random Bits. In: Calude, C.S., Kari, J., Petre, I., Rozenberg, G. (eds) Unconventional Computation. UC 2011. Lecture Notes in Computer Science, vol 6714. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21341-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-21341-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21340-3

  • Online ISBN: 978-3-642-21341-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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