Leftover hashing from quantum error correction: Unifying the two approaches to the security proof of quantum key distribution

TL;DR

This paper unifies two major approaches to proving the security of quantum key distribution by linking the leftover hashing lemma with quantum error correction codes, simplifying the theoretical framework.

Contribution

It demonstrates the equivalence of the Mayers-Shor-Preskill and Renner approaches, connecting security proofs with quantum error correction and the leftover hashing lemma.

Findings

Established a direct connection between the leftover hashing lemma and quantum error correction codes.

Proved the equivalence of two major security proof approaches for QKD.

Simplified the theoretical understanding of QKD security proofs.

Abstract

We show that the Mayers-Shor-Preskill approach and Renner's approach to proving the security of quantum key distribution (QKD) are essentially the same. We begin our analysis by considering a special case of QKD called privacy amplification (PA). PA itself is an important building block of cryptography, both classical and quantum. The standard theoretical tool used for its security proof is called the leftover hashing lemma (LHL). We present a direct connection between the LHL and the coding theorem of a certain quantum error correction code. Then we apply this result to proving the equivalence between the two approaches to proving the security of QKD.