# The m-least significant bits operation for quantum random number generation

## TL;DR

This paper analyzes the m-least significant bits operation in quantum random number generators, providing a physical explanation and evaluating its effectiveness under different source trust scenarios.

## Contribution

It introduces a new POVM-based explanation for the m-LSBs operation and assesses its randomness extraction capabilities in trusted and untrusted source scenarios.

## Key findings

- Effective in trusted source scenarios
- Ineffective in untrusted source scenarios
- Provides a new physical interpretation of m-LSBs operation

## Abstract

Quantum random number generators (QRNGs) can provide genuine randomness based on the inherent unpredictable nature of quantum physics. The extracted randomness relies not only on the physical parts of the QRNG, such as the entropy source and the measurement device, but also on appropriate postprocessing method. The m-least significant bits (m-LSBs) operation is one of the simplest randomness extraction method, which has the advantage of easy implementations. Nonetheless, a detailed analysis of the m-LSBs operation in QRNGs is still missing. In this work we give a physical explanation of the m-LSBs operation by introducing a new positive operator-valued measurement operator, which is obtained by regrouping the results of coarse-grained measurements. Both trusted and untrusted source scenarios are discussed. The results show that the m-LSBs operation can extract randomness effectively under the condition of the trusted source, while it is not effective under the untrusted source scenario.