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Security of Quantum Key Distribution

Renato Renner

TL;DR

The thesis develops a robust, non-iid security framework for quantum key distribution (QKD) by introducing smooth min- and max-entropies and a finite de Finetti representation for symmetric states. It proves a universal security criterion showing that coherent attacks do not outperform collective attacks, and that QKD keys can be safely used in any application under composable security guarantees. The work yields explicit non-asymptotic bounds on finite-key secrecy, improves practical protocol bounds (e.g., BB84 and six-state schemes), and applies to continuous-variable and noisy-device scenarios. Overall, the approach provides a general, operational foundation for secure quantum key distillation and robust, composable cryptographic security in realistic quantum networks.

Abstract

We propose various new techniques in quantum information theory, including a de Finetti style representation theorem for finite symmetric quantum states. As an application, we give a proof for the security of quantum key distribution which applies to arbitrary protocols.

Security of Quantum Key Distribution

TL;DR

The thesis develops a robust, non-iid security framework for quantum key distribution (QKD) by introducing smooth min- and max-entropies and a finite de Finetti representation for symmetric states. It proves a universal security criterion showing that coherent attacks do not outperform collective attacks, and that QKD keys can be safely used in any application under composable security guarantees. The work yields explicit non-asymptotic bounds on finite-key secrecy, improves practical protocol bounds (e.g., BB84 and six-state schemes), and applies to continuous-variable and noisy-device scenarios. Overall, the approach provides a general, operational foundation for secure quantum key distillation and robust, composable cryptographic security in realistic quantum networks.

Abstract

We propose various new techniques in quantum information theory, including a de Finetti style representation theorem for finite symmetric quantum states. As an application, we give a proof for the security of quantum key distribution which applies to arbitrary protocols.

Paper Structure

This paper contains 142 sections, 85 theorems, 451 equations.

Table of Contents

  1. Introduction
  2. Motivation
  3. Quantum key distribution: general facts
  4. Cryptographic setting
  5. Key agreement by quantum communication
  6. An example: the BB84 protocol
  7. Alternative protocols
  8. QKD over noisy channels
  9. Quantum key distribution and distillation
  10. Contributions
  11. New notions in quantum information theory
  12. Smooth min- and max-entropies as generalizations of von Neumann entropy
  13. De Finetti representation theorem for finite symmetric quantum states
  14. Universal security of keys in a quantum world
  15. Security of privacy amplification against quantum adversaries
  16. ...and 127 more sections

Key Result

Proposition 2.1.1

Let $P, P' \in \mathcal{P}(\mathcal{X})$ be probability distributions. Then there exists a joint distribution $P_{X X'}$ such that $P$ and $P'$ are the marginals of $P_{X X'}$ (i.e., $P = P_X$, $P' = P_{X'}$) and, for $(x,x')$ chosen according to $P_{X X'}$,

Theorems & Definitions (195)

  • Proposition 2.1.1
  • Definition 3.1.1
  • Definition 3.1.2
  • Remark 3.1.3
  • Remark 3.1.4
  • Lemma 3.1.5
  • proof
  • Lemma 3.1.6
  • proof
  • Lemma 3.1.7
  • ...and 185 more