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Processing Entangled Links Into Secure Cryptographic Keys

Marcel Kokorsch, Guido Dietl

TL;DR

The paper addresses how to maximize secure key rate in entanglement-based QKD by modeling the full processing chain from entangled-link generation through distillation and measurement to classical postprocessing. It adopts a unified framework, using Werner-state modeling and the Devetak–Winter rate, to derive optimal measurement bases, proposes asymmetric and symmetric processing strategies, and analyzes how many entanglement-distillation iterations are beneficial. A key finding is the fidelity threshold $F_{th} \approx 0.8107$ for positive key rate under optimal bases, and a comparative advantage of the symmetric strategy for certain noise levels ($\eta < 0.0625$) and fidelities. The work also provides a practical method to estimate the optimal distillation depth $k_{opt}$ and discusses how post-distillation state shapes (Bell-diagonal vs Werner) influence the results, offering a quantitative pathway to optimize end-to-end entanglement-based QKD implementations.

Abstract

The following paper presents a holistic approach to the processing of entangled links within entanglement based quantum key distribution protocols, whose security relies on the Bell inequality. We investigate the interactions, and the collective impact, of the whole processing chain on the final secure key rate. This includes the quantum mechanical preprocessing in the form of entanglement distillation, processing of the entangled states via measurements and the necessary classical postprocessing based on the measurement results. Our investigations are based on the principle idea of the Eckert 1991 protocol and utilize the secret key capacity introduced by Devetak and Winter in 2005. Our results include a proof on what measurement bases need to be chosen to achieve this capacity for the case of Werner states. It also presents a new processing strategy and compares it with the most common one that can be found within the literature. Furthermore, it answers the question on how much entanglement distillation is optimal. By doing so we propose a unified formalism, describing the whole processing chain, that can be used to make quantitative statements on the relation between the quality and quantity of entangled but noisy quantum states used for generating secure keys.

Processing Entangled Links Into Secure Cryptographic Keys

TL;DR

The paper addresses how to maximize secure key rate in entanglement-based QKD by modeling the full processing chain from entangled-link generation through distillation and measurement to classical postprocessing. It adopts a unified framework, using Werner-state modeling and the Devetak–Winter rate, to derive optimal measurement bases, proposes asymmetric and symmetric processing strategies, and analyzes how many entanglement-distillation iterations are beneficial. A key finding is the fidelity threshold for positive key rate under optimal bases, and a comparative advantage of the symmetric strategy for certain noise levels () and fidelities. The work also provides a practical method to estimate the optimal distillation depth and discusses how post-distillation state shapes (Bell-diagonal vs Werner) influence the results, offering a quantitative pathway to optimize end-to-end entanglement-based QKD implementations.

Abstract

The following paper presents a holistic approach to the processing of entangled links within entanglement based quantum key distribution protocols, whose security relies on the Bell inequality. We investigate the interactions, and the collective impact, of the whole processing chain on the final secure key rate. This includes the quantum mechanical preprocessing in the form of entanglement distillation, processing of the entangled states via measurements and the necessary classical postprocessing based on the measurement results. Our investigations are based on the principle idea of the Eckert 1991 protocol and utilize the secret key capacity introduced by Devetak and Winter in 2005. Our results include a proof on what measurement bases need to be chosen to achieve this capacity for the case of Werner states. It also presents a new processing strategy and compares it with the most common one that can be found within the literature. Furthermore, it answers the question on how much entanglement distillation is optimal. By doing so we propose a unified formalism, describing the whole processing chain, that can be used to make quantitative statements on the relation between the quality and quantity of entangled but noisy quantum states used for generating secure keys.

Paper Structure

This paper contains 13 sections, 9 theorems, 59 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Entangled Link Generation
  4. Preprocessing via Entanglement Distillation
  5. Entangled State Processing
  6. Postprocessing Based Key Distillation Capacity
  7. Optimal Measurement Bases $\mathcal{B}_A$ and $\mathcal{B}_B$
  8. Processing Strategies
  9. Asymmetric Processing Strategy
  10. Symmetric Processing Strategy
  11. Optimal Amount of Entanglement Distillation
  12. Consideration of Post Distillation Shape
  13. Conclusion and Outlook

Key Result

Proposition 1

The von Neumann entropy of the conditional post measurement state $\varrho_B^a$, that results from A measuring the state $\varrho_{AB} \in \mathcal{D}_\mathrm{B}(\mathcal{H}_{AB})$ within the orthonormal basis $\mathcal{B}_A = \{\ket{\alpha},\ket{\alpha^\perp}\}$, depends on the chosen measurement b

Figures (1)

  • Figure 1: Region map comparing the two processing strategies, dependent on the values for $\eta$ and $F(\varrho_{AB})$, and for the assumption that $\varrho \in \mathcal{D}_\mathrm{W}(\mathcal{H}_{AB})$.

Theorems & Definitions (18)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • Proposition 5
  • proof
  • ...and 8 more