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Device independent quantum key distribution with robust self-tests

Andreas Bluhm, Gereon Koßmann, René Schwonnek

Abstract

Device-independent quantum key distribution (DIQKD) provides a model of quantum key distribution with minimal assumptions and highly abstract theoretical building blocks. Although DIQKD frees us from detailed discussions of specific device models and associated error parameters, it replaces them with fundamental assumptions about the validity of quantum experiments. In this work, we propose a way to lift a protocol based on DIQKD-style assumptions to a device-dependent QKD protocol by performing local self-tests in the laboratories of the two key-generating parties. In particular, we consider routed Bell-test setups as a means of self-testing the local parties in earnest and develop a rigorous mathematical framework showing that the underlying optimization problems can indeed be transferred to the device-dependent QKD setting. As an application, we illustrate many of the relevant techniques through the case study of a routed BB84 protocol.

Device independent quantum key distribution with robust self-tests

Abstract

Device-independent quantum key distribution (DIQKD) provides a model of quantum key distribution with minimal assumptions and highly abstract theoretical building blocks. Although DIQKD frees us from detailed discussions of specific device models and associated error parameters, it replaces them with fundamental assumptions about the validity of quantum experiments. In this work, we propose a way to lift a protocol based on DIQKD-style assumptions to a device-dependent QKD protocol by performing local self-tests in the laboratories of the two key-generating parties. In particular, we consider routed Bell-test setups as a means of self-testing the local parties in earnest and develop a rigorous mathematical framework showing that the underlying optimization problems can indeed be transferred to the device-dependent QKD setting. As an application, we illustrate many of the relevant techniques through the case study of a routed BB84 protocol.

Paper Structure

This paper contains 17 sections, 10 theorems, 189 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Models
  3. Security assumptions and switches
  4. Comparing statistics
  5. Short-range quantum correlations in the multipartite setting
  6. Robust lifts of DIQKD to device-dependent QKD
  7. Routed BB84 protocol
  8. General robust self-testing and conditional von Neumann entropies
  9. General lifts of device-independent tasks
  10. Error bounds for robust self-tests
  11. A DIQKD protocol and finite-size analysis
  12. The Protocol
  13. Theoretical application of Renyi-entropy accumulation and secrecy
  14. Outlook
  15. Acknowledgments
  16. ...and 2 more sections

Key Result

Proposition 2

In the device independent setting are both models eq:our_channel_model and eq:pironio_channel_model equivalent. That means, given a state $\rho_{ABF}$ as an output state of the first model, then there exists a channel of the second model and an input state $\tau_{AA^\prime T}$ of the second model su

Figures (2)

  • Figure 1: (a) Figure adapted from Lobo2024. In this model the switch and the source are treated as different devices that do not influence each other. The source creates a fixed state. Controlled by a random variable $Z$, the Bob part of this state is either routed to $Bob_{short}$ or to $Bob_{long}$ via the switch. (b) Figure adapted from kossmann2025routedbelltestsarbitrarily. Here the action of the switch is modeled as part of the source, which now has an extra classical parameter $T_A$ as input.
  • Figure 2: Adapted from the setting in kossmann2025routedbelltestsarbitrarily. A routed Bell experiment with four parties. The self-tests are performed by the pairs Alice-Fred and Bob-George.

Theorems & Definitions (23)

  • Example 1: Assumptions on switch
  • Proposition 2
  • proof
  • Corollary 3
  • Proposition 4
  • proof
  • Definition 5: Effective overlap
  • Lemma 6: Continuity of the effective overlap in the marginal state
  • proof
  • Definition 7: Robust self-test
  • ...and 13 more