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On High-Dimensional Twin-Field Quantum Key Distribution

Ronny Müller, Mujtaba Zahidy, Leif Katsuo Oxenløwe, Søren Forchhammer, Davide Bacco

TL;DR

This paper analyzes the possibility of extending Twin-Field QKD to higher dimensions. It formalizes a high-dimensional TF-QKD framework based on single-photon states encoded in coefficient vectors, then proves that, under strict assumptions of single-photon encoding, independence, and zero residual error, high-dimensional TF-QKD is impossible for $N_A>2$ or $N_B>2$ due to intrinsic state-structure ambiguities. A 4D motivational example illustrates how increased dimensionality introduces unavoidable systematic errors and limits information per photon, while the discussion connects these results to measurement constraints and related SNS variants. The Supplements further conjecture that allowing any nonzero systematic error still cannot yield $l>1$ per symbol, reinforcing the claim that HD-TF-QKD cannot achieve the hallmark square-root scaling in higher dimensions. Overall, the work delineates fundamental limits on HD-TF-QKD within the proposed formalism and motivates future exploration of alternative approaches for long-distance high-dimensional QKD.

Abstract

Twin-Field Quantum Key Distribution (QKD) is a QKD protocol that uses single-photon interference to perform QKD over long distances. QKD protocols that encode information using high-dimensional quantum states can benefit from increased key rates and higher noise resilience. We define the essence of Twin-Field QKD and explore its generalization to higher dimensions. Further, we show that, ultimately, the Twin-Field protocol cannot be generalized to higher dimensions in accordance with our definition.

On High-Dimensional Twin-Field Quantum Key Distribution

TL;DR

This paper analyzes the possibility of extending Twin-Field QKD to higher dimensions. It formalizes a high-dimensional TF-QKD framework based on single-photon states encoded in coefficient vectors, then proves that, under strict assumptions of single-photon encoding, independence, and zero residual error, high-dimensional TF-QKD is impossible for or due to intrinsic state-structure ambiguities. A 4D motivational example illustrates how increased dimensionality introduces unavoidable systematic errors and limits information per photon, while the discussion connects these results to measurement constraints and related SNS variants. The Supplements further conjecture that allowing any nonzero systematic error still cannot yield per symbol, reinforcing the claim that HD-TF-QKD cannot achieve the hallmark square-root scaling in higher dimensions. Overall, the work delineates fundamental limits on HD-TF-QKD within the proposed formalism and motivates future exploration of alternative approaches for long-distance high-dimensional QKD.

Abstract

Twin-Field Quantum Key Distribution (QKD) is a QKD protocol that uses single-photon interference to perform QKD over long distances. QKD protocols that encode information using high-dimensional quantum states can benefit from increased key rates and higher noise resilience. We define the essence of Twin-Field QKD and explore its generalization to higher dimensions. Further, we show that, ultimately, the Twin-Field protocol cannot be generalized to higher dimensions in accordance with our definition.
Paper Structure (8 sections, 31 equations, 1 figure, 3 tables)

This paper contains 8 sections, 31 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Twin-Field QKD in 2 dimensions
  3. Motivational Example of Twin-Field in 4 Dimensions
  4. Assumptions
  5. Main Theorem and Proofs
  6. Discussion
  7. Conclusion
  8. Supplements

Figures (1)

  • Figure 1: Possible abstract setups for a Twin-Field QKD protocol, for 2 dimensions (left) and 4 dimensions (right). SPS: Single photon source, MPBS: Multi-port beamsplitter.