Quantum GHZ Multiplexer: Hierarchical Teleportation for 1→2ⁿ Quantum Networks

We introduce a quantum multiplexer (GHZ MUX) architecture that enables deterministic routing of an unknown qubit from a single sender to one of 2n receivers using only local tripartite Greenberger-Horne-Zeilinger (GHZ) states arranged in a binary tree. At each level of the hierarchy, a Bell-basis measurement and classical feed-forward propagate the encoded quantum information along a selected branch while maintaining the appropriate Pauli correction frame. Unlike quantum routing architectures that rely on globally entangled multipartite states, the proposed design composes small GHZ clusters into a modular teleportation hierarchy that requires only local entanglement generation and coherence. This structure achieves full input-output connectivity while preserving deterministic routing control and experimental feasibility for near-term small-scale quantum networks. Beyond routing functionality, we show that the same GHZ-tree structure naturally supports hidden-destination communication. We formalize this extension as the Hidden-Secret GHZ-Tree Routing (HS-GTR) protocol, in which the final receiver remains unknown to external observers and the transmitted quantum state may optionally be protected by a quantum one-time pad. This construction demonstrates that hierarchical GHZ routing can serve not only as a quantum switching architecture but also as a building block for privacy-preserving communication and multi-receiver key establishment in distributed quantum networks.