A coherence-witnessing game and applications to semi-device-independent quantum key distribution

Mário Silva1, Ricardo Faleiro2, Paulo Mateus2,3, and Emmanuel Zambrini Cruzeiro2

1Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
2Instituto de Telecomunicações, 1049-001, Lisbon, Portugal
3Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais 1049-001, Lisbon, Portugal

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Semi-device-independent quantum key distribution aims to achieve a balance between the highest level of security, device independence, and experimental feasibility. Semi-quantum key distribution presents an intriguing approach that seeks to minimize users' reliance on quantum operations while maintaining security, thus enabling the development of simplified and hardware fault-tolerant quantum protocols. In this work, we introduce a coherence-based, semi-device-independent, semi-quantum key distribution protocol built upon a noise-robust version of a coherence equality game that witnesses various types of coherence. Security is proven in the bounded quantum storage model, requiring users to implement only classical operations, specifically fixed-basis detections.

Device-independent cryptography aims to establish security with minimal assumptions about the devices used. Alternatively, the goal of the semi-quantum perspective is to reduce users' reliance on quantum operations while still ensuring security based on the principles of quantum mechanics. In this work, we extend a coherence equality game to a noise-robust scenario and demonstrate its capability to statistically differentiate between three types of coherence resources: non-coherent, separable coherent, and entangled coherent states. Building upon the game, we present a proof-of-concept quantum key distribution protocol. In this protocol, Alice and Bob only need to perform trusted particle detections within their labs, while the remaining components of the protocol are considered untrusted. Consequently, this protocol can be accurately characterized as both semi-device-independent and semi-quantum, showcasing the compatibility of both frameworks.

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Cited by

[1] Julia Guskind and Walter O. Krawec, "Mediated semi-quantum key distribution with improved efficiency", Quantum Science and Technology 7 3, 035019 (2022).

[2] Saachi Mutreja and Walter O. Krawec, "Improved semi-quantum key distribution with two almost-classical users", Quantum Information Processing 21 9, 319 (2022).

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