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A quantum random number generator certified by value indefiniteness

Published online by Cambridge University Press:  28 March 2014

ALASTAIR A. ABBOTT ,
CRISTIAN S. CALUDE  and
KARL SVOZIL
ALASTAIR A. ABBOTT
Affiliation:
Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand Email: a.abbott@auckland.ac.nz; cristian@cs.auckland.ac.nz
CRISTIAN S. CALUDE
Affiliation:
Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand Email: a.abbott@auckland.ac.nz; cristian@cs.auckland.ac.nz
KARL SVOZIL
Affiliation:
Institut für Theoretische Physik, Vienna University of Technology, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria Email: svozil@tuwien.ac.at
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Abstract

In this paper we propose a quantum random number generator (QRNG) that uses an entangled photon pair in a Bell singlet state and is certified explicitly by value indefiniteness. While ‘true randomness’ is a mathematical impossibility, the certification by value indefiniteness ensures that the quantum random bits are incomputable in the strongest sense. This is the first QRNG setup in which a physical principle (Kochen–Specker value indefiniteness) guarantees that no single quantum bit that is produced can be classically computed (reproduced and validated), which is the mathematical form of bitwise physical unpredictability.

We discuss the effects of various experimental imperfections in detail: in particular, those related to detector efficiencies, context alignment and temporal correlations between bits. The analysis is very relevant for the construction of any QRNG based on beam-splitters. By measuring the two entangled photons in maximally misaligned contexts and using the fact that two bitstrings, rather than just one, are obtained, more efficient and robust unbiasing techniques can be applied. We propose a robust and efficient procedure based on XORing the bitstrings together – essentially using one as a one-time-pad for the other – to extract random bits in the presence of experimental imperfections, as well as a more efficient modification of the von Neumann procedure for the same task. We also discuss some open problems.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Special Issue 3: Developments of the Concepts of Randomness, Statistic and Probability , June 2014 , e240303
Copyright
Copyright © Cambridge University Press 2014 

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