# Sampling in a Quantum Population, and Applications

## TL;DR

This paper introduces a framework for analyzing classical sampling strategies when applied to quantum systems, enabling new security proofs for quantum cryptographic protocols.

## Contribution

It provides a method to interpret and evaluate the accuracy of classical sampling strategies in quantum settings, linking their quantum and classical performances.

## Key findings

- New framework for quantum sampling analysis
- Simplified security proofs for quantum cryptography schemes
- Enhanced understanding of classical-quantum sampling accuracy

## Abstract

We propose a framework for analyzing classical sampling strategies for estimating the Hamming weight of a large string, when applied to a multi-qubit quantum system instead. The framework shows how to interpret such a strategy and how to define its accuracy when applied to a quantum system. Furthermore, we show how the accuracy of any strategy relates to its accuracy in its classical usage, which is well understood for the important examples. We show the usefulness of our framework by using it to obtain new and simple security proofs for the following quantum-cryptographic schemes: quantum oblivious-transfer from bit-commitment, and BB84 quantum-key-distribution.