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Journal of the Optical Society of America B

Search for patterns in sequences of single-photon polarization measurements

David A. Branning, Adam Katcher, Wayne Strange, Mark P. Silverman

Published May 18, 2011• 4 citations
Publisher

Abstract

Sequences of random binary numbers created from polarization measurements of single photons were subjected to a comprehensive runs analysis. Photon pairs from a spontaneous parametric downconversion source were detected in coincidence, with one photon acting as a trigger while the other was analyzed for horizontal or vertical polarization. The resulting sequences of polarization measurements were tested for runs of consecutive vertical or horizontal outcomes against a theory of nonoverlapping runs, without numerical unbiasing. The sequences produced no statistically significant discrepancies with the predicted numbers of runs, even with multiphoton events retained.

DOI
10.1364/josab.28.001423

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Sequences of random binary numbers created from polarization measurements of single photons were subjected to a comprehensive runs analysis. Photon pairs from a spontaneous parametric downconversion source were detected in coincidence, with one photon acting as a trigger while the other was analyzed for horizontal or vertical polarization. The resulting sequences of polarization measurements were tested for runs of consecutive vertical or horizontal outcomes against a theory of nonoverlapping runs, without numerical unbiasing. The sequences produced no statistically significant discrepancies with the predicted numbers of runs, even with multiphoton events retained.
A binary sequence was constructed from 1.7×107 polarization measurements of single photons from a spontaneous parametric downconversion source, under pumping conditions similar to those used in optical quantum cryptography. To search for correlations in the polarization measurement outcomes, we subjected the sequence to a suite of tests developed at the National Institute of Standards and Technology (NIST) for the assessment of algorithmic random-number generators. The bias of the sequence was low enough to allow all fifteen tests to be applied directly to the polarization outcomes without using any numerical unbiasing procedures. No statistically significant deviations from randomness were observed, other than those related to this small uncorrected bias.
In this letter, we present an implementation of a random number generator based on photon polarization superposition. We prepare photons in a superposition state of vertical and horizontal polarizations, let them pass through a polarizing beamsplitter and set two detectors at each path to get a 50–50 chance of finding the photon at each detector. We present the results of the NIST test suite for random number generators for our binary sequence of approximately 1.4 × 107 bits and analyze the different p-values obtained to statistically assess its randomness. In doing so, we use von Neumann’s algorithm for bias removal and briefly explain how the statistical tests work.
A new scheme for a random number generator based on quantum entangled photon pairs is demonstrated. Signal photons produced by optical parametric down-conversion are detected at two single-photon detectors after transmission or reflection at a 50/50% beamsplitter, to form a truly random binary sequence. Their arrival is signalled by their twin idler photons, so that a cw laser source may be used instead of attenuated laser pulses. Coincidence measurement is employed to obtain the bit sequences, which are shown to fully satisfy the standard tests for randomness.