What question did this study set out to answer?

This study aims to present a high-dimensional quantum key agreement protocol that ensures security, fairness, and tolerance to losses among multiple users.

April 25, 2026Open Access

High-dimensional GHZ-based multi-party quantum key agreement: rigorous security, fairness, and loss tolerance

Key Points

This study aims to present a high-dimensional quantum key agreement protocol that ensures security, fairness, and tolerance to losses among multiple users.
Developed a GHZ-based protocol utilizing N-partite d-level states in a star topology with a commit-then-reveal mechanism.
Analyzed channel noise effects, including phase and amplitude damping, to validate protocol robustness through Monte Carlo simulations.
Modelled various errors and correlated them with security metrics and entropy bounds to ensure composable secrecy.
Confirmed that using d>2 improves the positive-rate region and reduces the survival threshold for throughput relative to standard qubit protocols.
Achieved rigorous fairness with equal influence and strict guarantees against unfair outcomes in key distribution.
Demonstrated potential for implementation through various photonic techniques, addressing practical challenges for scaling.

Abstract

Abstract Multi-party quantum key agreement (MQKA) enables a group of mutually untrusted users to jointly establish a secret key with equal influence, a capability not provided by two-party quantum key distribution (QKD) and increasingly relevant for securing resilient infrastructure such as quantum-enabled smart grid networks and distributed cyber-physical systems. We present a high-dimensional Greenberger-Horne-Zeilinger (GHZ) -based MQKA that simultaneously targets rigorous security, provable fairness, and practical loss tolerance. The protocol distributes an N -partite d -level GHZ state in a star (with an optional star-of-stars hierarchy for large N) and maps each user’s contribution to local X₃^a Z₃^b X d a Z d b operations. A commit-then-reveal layer makes inputs binding and hiding, yielding equal influence fairness over Z₃ Z d with a strict fair-abort guarantee. Composable secrecy is established via entropy bounds and a Devetak-Winter-style key rate analysis, strengthened by test-round statistics; we connect Mermin/Svetlichny-type correlators to min-entropy lower bounds and incorporate full leakage accounting and finite-key penalties. We model depolarizing, shift/phase (Weyl), amplitude-damping, erasures, detector efficiency, and dark counts, and derive closed-form mappings from device parameters to symbol/phase errors. Monte Carlo studies confirm that d>2 d > 2 expands the positive-rate region and reduces the global survival required for a given throughput compared with qubit GHZ MQKA under identical conditions. We discuss potential photonic realizations (time-bin or frequency-bin encoding, discrete Fourier transform networks, and superconducting nanowire detectors) and architectural pathways toward larger N via hierarchical clustering, while acknowledging the significant technological challenges that would need to be overcome to realize high-dimensional multipartite entanglement experimentally. Overall, the scheme delivers higher efficiency per entangled state, rigorous fairness, and composable security with realistic noise and loss, addressing key gaps in current MQKA designs for resilient infrastructure.

Bookmark

View Full Paper

Cite This Study

Sohail et al. (Thu,) studied this question.

synapsesocial.com/papers/69ec5a4488ba6daa22dabc7e https://doi.org/https://doi.org/10.1140/epjqt/s40507-026-00510-1

Bookmark

View Full Paper