An Observed-Data-Consistent Approach to the Assignment of Bit Values in a Quantum Random Number Generator

TL;DR

This paper introduces a Bayesian inference-based method for assigning bit values in quantum random number generators, reducing bias and improving real-time bias control compared to traditional maximum likelihood approaches.

Contribution

It presents a novel Bayesian approach to convert quantum measurement data into unbiased random bits, addressing biases from conventional parameter estimation methods.

Findings

Bayesian method reduces binning bias in QRNG data.

Automatically controls bias in real-time during data acquisition.

Limits the maximum achievable bit rate based on measurement record.

Abstract

The majority of Quantum Random Number Generators (QRNG) are designed as converters of a continuous quantum random variable into a discrete classical random bit value. For the resulting random bit sequence to be minimally biased, the conversion process demands an experimenter to fully characterize the underlying quantum system and implement parameter estimation routines. Here we show that conventional approaches to parameter estimation (such as e.g. {\it Maximum Likelihood Estimation}) used on a finite QRNG data sample without caution may introduce binning bias and lead to overestimation of the randomness of the QRNG output. To bypass these complications, we develop an alternative conversion approach based on the Bayesian statistical inference method. We illustrate our approach using experimental data from a time-of-arrival QRNG and numerically simulated data from a vacuum homodyning QRNG. Side-by-side comparison with the conventional conversion technique shows that our method provides an automatic on-line bias control and naturally bounds the best achievable QRNG bit rate for a given measurement record.