Equivalence of three classical algorithms with quantum side information: Privacy amplification, error correction, and data compression

TL;DR

This paper demonstrates the equivalence of privacy amplification, error correction, and data compression algorithms with quantum side information in the one-shot setting, leading to new security bounds and simplified proofs in quantum cryptography.

Contribution

It establishes the equivalence of three fundamental algorithms with quantum side information and applies this to improve quantum key distribution security proofs.

Findings

Equivalence of PA, EC, and DC algorithms with quantum side information.

Translated security bounds of PA into new coding theorems for EC and DC.

Simplified and improved the security proof approach for QKD.

Abstract

Privacy amplification (PA) is an indispensable component in classical and quantum cryptography. Error correction (EC) and data compression (DC) algorithms are also indispensable in classical and quantum information theory. We here study these three algorithms (PA, EC, and DC) in the presence of quantum side information, and show that they all become equivalent in the one-shot scenario. As an application of this equivalence, we take previously known security bounds of PA, and translate them into coding theorems for EC and DC which have not been obtained previously. Further, we apply these results to simplify and improve our previous result that the two prevalent approaches to the security proof of quantum key distribution (QKD) are equivalent. We also propose a new method to simplify the security proof of QKD.