  Quantum Conference Key Agreement (QCKA) protocols are designed to allow
multiple parties to agree on a shared secret key, secure against
computationally unbounded adversaries. In this paper, we consider a
high-dimensional QCKA protocol and prove its information theoretic security
against arbitrary, general, attacks in the finite-key scenario. Our proof
technique may be useful for other high-dimensional multi-party quantum
cryptographic protocols. Finally, we evaluate the protocol in a variety of
settings, showing that high-dimensional states can greatly benefit QCKA
protocols.
