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EPJ Quantum Technology

On the randomness of time ordered quantum measurements

Jonas Almlöf, Thomas Lettner, Samuel Gyger, Gemma Vall-llosera, Tigge Nilsson, Val Zwiller

Published Nov 25, 2024• 1 citation
Publisher

Abstract

Abstract A new method for efficient, high-quality randomness extraction is presented. The method relies on quantum processes such as the emission of single photons and their subsequent detection, where each detection event has an associated detection time. We show that, by utilising the number of possibilities to arrange a timed quantum measurement sequence, the efficiency can be increased many-fold compared to current methods. The method delivers fundamentally uniform randomness and therefore does not need any post processing or de-biasing.

DOI
10.1140/epjqt/s40507-024-00288-0

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Abstract Quantum random number generators with a continuous variable are considered based on a primary randomness of the outcomes of homodyne measurements of a coherent state. A deterministic method of extraction of truly random 0 and 1 from the primary sequence of measurements of the quadrature of the field in homodyne detection is considered. The method, in the case of independence of successive measurement outcomes, in the asymptotic limit of long sequences, allows us to extract with a polynomial complexity all the true randomness contained in the primary sequence. The method does not require knowledge of the probability distribution function of the primary random sequence, and also does not require additional randomness in the extraction of random 0 and 1. The approach with deterministic randomness extractors, unlike other methods, contains fewer assumptions and conditions that need to be satisfied in the experimental implementation of such generators, and is significantly more effective and simple in experimental implementation. The fundamental limitations dictated by nature for achieving statistical independence of successive measurement outcomes are also considered. The statistical independence of the measurement outcomes is the equivalent of true randomness, in the sense that is possible in the case of the independence of the measurement outcomes, provably, with deterministic extractor, to extract a ‘truly random sequence of 0 and 1’. It is shown that in the asymptotic limit it is possible to extract all the true randomness contained in the outcomes of physical measurements.