Protocols for teleporting a cat state via a high-dimensional entangled state

This study advances economical Quantum Teleportation (QT) schemes for cat states across arbitrary dimensional Hilbert spaces. First, we develop a protocol for teleporting an unknown two-dimensional cat state using a three-dimensional maximally entangled three-qutrit quantum channel. The approach involves constructing a complete orthogonal nonsymmetric measurement basis, where the sender performs joint measurements on three particles. The receiver then applies dimension-specific unitary operations conditioned on measurement outcomes to reconstruct the target state. Subsequently, we extend this protocol by replacing the maximally entangled channel with a nonmaximally entangled three-qutrit state. Through auxiliary qubit introduction and optimized operations, the two-qubit cat state is probabilistically recovered. We derive the success probability for both protocols, demonstrating that the nonmaximally entangled case generalizes the former scheme. Further generalization is achieved through two nonsymmetric basis constructions: (i) Scaling quantum channel dimension from 3 to [Formula: see text] dimensions; (ii) Extending transmitted cat states from 2 to [Formula: see text] dimensions [Formula: see text]. These dual-dimensional generalizations establish distinct economical advantages over existing QT schemes.