Quantum Sampling for Optimistic Finite Key Rates in High Dimensional Quantum Cryptography

TL;DR

This paper advances quantum sampling-based entropic uncertainty relations, enhancing security proofs for high-dimensional quantum cryptography and quantum random number generators, with new theoretical results and practical implications.

Contribution

It derives stronger, more powerful sampling-based entropic uncertainty relations and applies them to improve security analysis in high-dimensional quantum cryptography.

Findings

New entropic uncertainty relations derived

Applications to quantum random number generators

Asymptotic analysis of uncertainty relations

Abstract

It has been shown recently that the framework of quantum sampling, as introduced by Bouman and Fehr, can lead to new entropic uncertainty relations highly applicable to finite-key cryptographic analyses. Here we revisit these so-called sampling-based entropic uncertainty relations, deriving newer, more powerful, relations and applying them to source-independent quantum random number generators and high-dimensional quantum key distribution protocols. Along the way, we prove several interesting results in the asymptotic case for our entropic uncertainty relations. These sampling-based approaches to entropic uncertainty, and their application to quantum cryptography, hold great potential for deriving proofs of security for quantum cryptographic systems, and the approaches we use here may be applicable to an even wider range of scenarios.