High-dimensional Encoding in the Round-Robin Differential-Phase-Shift Protocol

Mikka Stasiuk1,2, Felix Hufnagel3,1, Xiaoqin Gao3,1, Aaron Z. Goldberg1,3, Frédéric Bouchard1, Ebrahim Karimi3,1, and Khabat Heshami1,3

1National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
2Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, N2L3G1 Waterloo, Ontario, Canada
3Nexus for Quantum Technologies, University of Ottawa, Ottawa, K1N 6N5, ON, Canada

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Abstract

In quantum key distribution (QKD), protocols are tailored to adopt desirable experimental attributes, including high key rates, operation in high noise levels, and practical security considerations. The round-robin differential phase shift protocol (RRDPS), falling in the family of differential phase shift protocols, was introduced to remove restrictions on the security analysis, such as the requirement to monitor signal disturbances, improving its practicality in implementations. While the RRDPS protocol requires the encoding of single photons in high-dimensional quantum states, at most, only one bit of secret key is distributed per sifted photon. However, another family of protocols, namely high-dimensional (HD) QKD, enlarges the encoding alphabet, allowing single photons to carry more than one bit of secret key each. The high-dimensional BB84 protocol exemplifies the potential benefits of such an encoding scheme, such as larger key rates and higher noise tolerance. Here, we devise an approach to extend the RRDPS QKD to an arbitrarily large encoding alphabet and explore the security consequences. We demonstrate our new framework with a proof-of-concept experiment and show that it can adapt to various experimental conditions by optimizing the protocol parameters. Our approach offers insight into bridging the gap between seemingly incompatible quantum communication schemes by leveraging the unique approaches to information encoding of both HD and DPS QKD.

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[1] Frank Schmidt, Daniel Miller, and Peter van Loock, "Error-corrected quantum repeaters with GKP qudits", arXiv:2303.16034, (2023).

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