Quantum teleportation using continuous-variable cluster states is a promising method for quantum state transmission. Experiments show photon subtraction improves the fidelity of two-mode-entangled state-based teleportation, but its effect on universal quantum teleportation with cluster states is unclear. This study clarifies this issue. We create a characteristic function-based representation for universal teleportation, combining it with the Hermite polynomial representation to analyze the impact of photon subtraction. Our analysis finds that the enhancement depends on the photon subtraction modes and the initial squeezing parameter of cluster states. Contrary to the two-mode case, subtracting photons from all cluster state modes does not improve fidelity. By analyzing the equivalent squeezing of initial states after photon subtraction, we determine that squeezing improvement decides teleportation quality. A remarkable finding reveals that performing photon subtraction on two modes of a multirail cluster state can enhance equivalent squeezing of all modes, offering new possibilities for quantum information processing tasks.

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• Optical quantum information processing
• Quantum entanglement
• Quantum information processing with continuous variables
• Quantum teleportation