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A Bipartite Quantum Key Distribution Protocol Based on Indefinite Causal Order

Mateusz Leśniak, Ryszard Kukulski, Paulina Lewandowska, Grzegorz Rajchel-Mieldzioć, Michał Wroński

Abstract

We propose a bipartite quantum key distribution (QKD) protocol based on causal nonseparability: the presence of a resource -- a process matrix -- that does not correspond to any definite causal order between two parties. In our protocol, Alice and Bob perform local operations arranged in a ``causal-order guessing game,'' whereby each round yields an 85.35\% probability of matching bits when the communication is undisturbed. This raw matching probability (or equivalently, a $\sim14.65\%$ error rate) is amenable to standard forward error-correction strategies. We further discuss the practical construction of the QKD protocol using indefinite causal order, where several different scenarios are deeply analyzed.

A Bipartite Quantum Key Distribution Protocol Based on Indefinite Causal Order

Abstract

We propose a bipartite quantum key distribution (QKD) protocol based on causal nonseparability: the presence of a resource -- a process matrix -- that does not correspond to any definite causal order between two parties. In our protocol, Alice and Bob perform local operations arranged in a ``causal-order guessing game,'' whereby each round yields an 85.35\% probability of matching bits when the communication is undisturbed. This raw matching probability (or equivalently, a error rate) is amenable to standard forward error-correction strategies. We further discuss the practical construction of the QKD protocol using indefinite causal order, where several different scenarios are deeply analyzed.
Paper Structure (21 sections, 28 equations, 2 figures, 3 tables)

This paper contains 21 sections, 28 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Overview of bipartite quantum key distribution protocols
  3. Quantum bit exchange based on indefinite causal order
  4. Bipartite process matrices
  5. Causal game setting
  6. Quantum bit exchange procedure based on causal game
  7. Security analysis of quantum bit exchange round procedure
  8. Threat model
  9. Estimating the efficiency of Eve
  10. Modeling as binary symmetric channel
  11. Quantum key exchange protocol
  12. Notation
  13. Protocol Description
  14. Setup phase
  15. Quantum bit exchange round
  16. ...and 6 more sections

Figures (2)

  • Figure 1: The figure shows the results of SDP optimization. On the $x$ axis we have the acceptance level as a parameter $Q$ and on the $y$ axis we have the probability $\mathbb{P}$ of key compliance for Alice and Bob (dashed red line) and for Eve and Alice (or Bob) (solid blue line).
  • Figure 2: Binary symmetric channel scheme.