Control power in controlled hybrid teleportation between a discrete-variable state and a continuous-variable state under decoherence effects

One of our works, [C. T. Bich and N. B. An, Pramana – Journal of Physics 96 (2022) 33], proposed a linear optics scheme for teleporting two different types of qubits. This was achieved by using a four-particle hybrid entangled state and controlled by two controllers operating in two distinct types of Hilbert spaces: a finite-dimensional space and an infinite-dimensional space. In this work, the power of the two controllers is assessed through the analysis of the average fidelity of the teleportation protocol in their absence. It is worth noting that the controller holding a discrete-variable state consistently exhibits power that is equal to or greater than that of the controller holding a continuous-variable state.