This protocol is a subroutine that allows the anonymous distribution of a GHZ state between $m+1$ parties, starting from an $n$-party GHZ state. It is used in the protocol: Anonymous Conference Key Agreement using GHZ states

Anonymous quantum conference key agreement

• The entanglement source generates and distributes sufficient GHZ states to all nodes in the network
• The GHZ states are distilled to establish multipartite entanglement shared only by the participating parties (the sender and receivers)

The ability to share a high-quality n-partite GHZ state

Network stage: entanglement generation

Other requirement:

• A broadcast channel
• A private randomness source

• $n$: Total number of nodes in the network
• $m$: Number of receiving nodes
• $k$-partite GHZ state: $\frac{1}{\sqrt{2}} \left( |0\rangle^{\otimes k} + |1\rangle^{\otimes k} \right)$

Anonymity

Input: $n$-partite GHZ state $\frac{1}{\sqrt{2}}(|0\rangle^{\otimes n} + |1\rangle^{\otimes n})$
Output: $(m+1)$-partite GHZ state $\frac{1}{\sqrt{2}}(|0\rangle^{\otimes (m+1)} + |1\rangle^{\otimes (m+1)})$ shared between the sender and receivers
Requirements: A broadcast channel; private randomness sources

• Sender and receiver draw a random bit each. Everyone else measures their qubits in the X-basis, yielding a measurement outcome bit $x_i$.
• All parties broadcast their bits in a random order, or if possible, simultaneously.
• The sender applies a Z gate to their qubit if the parity of the non-participating parties’ bits is odd.

1. Hahn, Frederik, Jarn de Jong, and Anna Pappa. “Anonymous quantum conference key agreement.” PRX Quantum 1, no. 2 (2020): 020325.
2. Mannalath, Vaisakh, and Anirban Pathak. “Multiparty entanglement routing in quantum networks.” Physical Review A 108, no. 6 (2023): 062614.