Quantum to Classical Randomness Extractors

TL;DR

This paper introduces quantum-to-classical randomness extractors (QC-extractors), demonstrating their construction using mutually unbiased bases and single qubit measurements, and applies them to entropic uncertainty relations and quantum cryptography security.

Contribution

It provides the first constructions of QC-extractors and links their properties to entropic uncertainty relations and quantum storage security.

Findings

QC-extractors constructed from MUBs and single qubit measurements

Established entropic uncertainty relations with quantum side information

Resolved the open problem in the noisy-storage security model

Abstract

The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness source, X is itself ultimately the result of a measurement on an underlying quantum system. When characterizing the power of a source to supply randomness it is hence a natural question to ask, how much classical randomness we can extract from a quantum system. To tackle this question we here take on the study of quantum-to-classical randomness extractors (QC-extractors). We provide constructions of QC-extractors based on measurements in a full set of mutually unbiased bases (MUBs), and certain single qubit measurements. As the first application, we show that any QC-extractor gives rise to entropic uncertainty relations with respect to quantum side information. Such relations were previously only known for two measurements. As the second application, we resolve the central open question in the noisy-storage model [Wehner et al., PRL 100, 220502 (2008)] by linking security to the quantum capacity of the adversary's storage device.