Performance optimization of continuous-variable quantum teleportation with generalized photon-varying non-Gaussian operations

Continuous variable quantum teleportation provides a path to the long-distance transmission of quantum states. Photon-varying non-Gaussian operations have been shown to improve the fidelity of quantum teleportation when integrated into the protocol. However, for a given type of non-Gaussian operation, the achievable fidelity varies with the parameters associated with the operation. Previous work only focused on particular settings of the parameters, over which an optimization was missing. The potential of such operations is not fully uncovered. Given a fixed non-Gaussian operation, the achievable fidelity also varies with input states. An operation that increases the fidelity for teleporting one class of states might do the contrary for other classes of states. A performance metric, upon which an operation is optimized, suitable for different input states, is also missing. In this work, we build a framework for photon-varying non-Gaussian operations for multimode states, upon which we propose a performance metric suitable for arbitrary teleportation input states. We then apply the new metric to evaluate different types of non-Gaussian operations. Starting from simple multiphoton photon subtraction and photon addition, we find that increasing the number of ancillary photons involved in the operation does not guarantee performance improvement. We then investigate a generalization of the operations mentioned above, finding that operations that approximate a particular form provide the best improvement. The results provided here will be valuable for real-world implementations of quantum teleportation networks and applications that harness the non-Gaussianity of quantum states.