Duality of privacy amplification against quantum adversaries and data compression with quantum side information

TL;DR

This paper reveals a fundamental duality between privacy amplification and data compression with quantum side information, linking them through quantum complementarity and uncertainty principles, with implications for quantum error correction.

Contribution

It establishes a novel duality between two key quantum information processing tasks, connecting classical primitives through quantum principles.

Findings

New uncertainty principle involving smooth min- and max-entropies

Conditions for approximate quantum error correction derived

Demonstrates the duality implies ability to perform one task enables the other

Abstract

We show that the tasks of privacy amplification against quantum adversaries and data compression with quantum side information are dual in the sense that the ability to perform one implies the ability to perform the other. These are two of the most important primitives in classical information theory, and are shown to be connected by complementarity and the uncertainty principle in the quantum setting. Applications include a new uncertainty principle formulated in terms of smooth min- and max-entropies, as well as new conditions for approximate quantum error correction.