A Quantum Random Number Generator Certified by Value Indefiniteness

TL;DR

This paper introduces a quantum random number generator certified by the principle of value indefiniteness, ensuring the generated bits are incomputable and physically unpredictable, with detailed analysis of experimental imperfections and robust extraction methods.

Contribution

It presents the first QRNG explicitly certified by Kochen-Specker value indefiniteness, guaranteeing the incomputability of generated bits and proposing robust unbiasing techniques.

Findings

The QRNG produces incomputable, truly random bits.

Experimental imperfections are thoroughly analyzed.

A robust XOR-based unbiasing method is proposed.

Abstract

In this paper we propose a quantum random number generator (QRNG) which utilizes 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 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 produced can be classically computed (reproduced and validated), the mathematical form of bitwise physical unpredictability. The effects of various experimental imperfections are discussed in detail, particularly those related to detector efficiencies, context alignment and temporal correlations between bits. The analysis is to a large extent relevant for the construction of any QRNG based on beam-splitters. By measuring the two entangled photons in maximally misaligned contexts and utilizing the fact that two rather than one bitstring are obtained, more efficient and robust unbiasing techniques can be applied. A robust and efficient procedure based on XORing the bitstrings together---essentially using one as a one-time-pad for the other---is proposed 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. Some open problems are also discussed.