Quantum Sampling and Entropic Uncertainty

TL;DR

This paper establishes a new connection between quantum sampling techniques and entropic uncertainty, leading to novel uncertainty relations and applications in quantum random number generation.

Contribution

It introduces a new entropic uncertainty relation based on quantum sampling, extending previous results and enabling applications in quantum randomness.

Findings

Derived a novel entropic uncertainty relation involving smooth min entropy and sampling probabilities.

Provided a simplified proof of a version of the Maassen-Uffink uncertainty relation.

Demonstrated applications to quantum random number generation.

Abstract

In this paper, we show an interesting connection between a quantum sampling technique and quantum uncertainty. Namely, we use the quantum sampling technique, introduced by Bouman and Fehr, to derive a novel entropic uncertainty relation based on smooth min entropy, the binary Shannon entropy of an observed outcome, and the probability of failure of a classical sampling strategy. We then show two applications of our new relation. First, we use it to develop a simple proof of a version of the Maassen and Uffink uncertainty relation. Second, we show how it may be applied to quantum random number generation.