Resource‐Optimal Four‐Party Cyclic Quantum Teleportation: A Rigorous Resource Bound and Deterministic Network Protocol

ABSTRACT

We formulate simultaneous four‐party cyclic quantum teleportation as an exact quantum‐channel simulation problem. Alice, Bob, Charlie, and David each hold an arbitrary input qubit and must transfer the four states in the directed cycle using only local operations, preshared entanglement, and classical communication. This formulation exposes a resource constraint that cannot be established from a recovery table alone. By testing the desired channel on inputs locally entangled with reference qubits, we prove that every exact deterministic realization must possess a Schmidt rank at least four, and at least two ebits across each one‐party‐versus‐three‐party bipartition. A resource containing only one qubit at each node, including a four‐qubit cluster state has local dimension two and therefore cannot implement the simultaneous transfer of four independent arbitrary qubits. For qubit resources, at least eight preshared resource qubits are necessary. We then construct a protocol that saturates this lower bound: four Bell pairs are placed on the directed network links, every sender performs one local Bell‐state measurement, and every receiver applies a two‐bit‐controlled Pauli correction. The complete recovery map contains joint outcomes but factorizes into four transparent four‐outcome maps, yielding a unit success probability and an irreducible classical record of eight bits. We further derive the induced cyclic Pauli channel for general Bell‐diagonal resources, distinguish link fidelity, product‐input fidelity, entanglement fidelity, and global average gate fidelity, and provide finite‐shot confidence formulas. All results are analytical or numerical; experimental requirements and platform‐specific limitations are discussed separately.