Continuous-variable (CV) quantum teleportation is usually benchmarked by average fidelity, but when the teleportation is repeatedly used within optical networks or measurement-based architectures, uniformity across the input ensemble becomes equally important. We analyze this issue using two complementary figures of merit: the average fidelity and the fidelity deviation, which quantifies the input dependence of the input-conditioned, outcome-averaged teleportation fidelity. We prove that any deterministic unity-gain teleportation channel that is displacement covariant has vanishing fidelity deviation for coherent-state benchmarking, irrespective of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation therefore diagnoses covariance breaking rather than non-Gaussianity. For a small nonuniform deformation away from a covariant baseline, we derive a local, protocol-dependent relation between the fidelity gain and the induced deviation; this relation is not a universal lower bound on probabilistic or non-Gaussian enhancements. As a concrete example, we study a measurement-based noiseless linear amplification inspired hard-window record-filtering surrogate. Within this model, the resulting trade-off among average fidelity, fidelity deviation, and success probability shows that stronger filtering can improve the conditional fidelity by concentrating the successful events in favored regions of phase space, thereby suppressing the success probability and reducing input uniformity. We further distinguish fidelity nonuniformity, quantified by $D$, from heralding selectivity, quantified by the input dependence of the success probability. Our results provide an operational framework for distinguishing genuine channel improvement from selectivity-driven postselected advantage and suggest that the probabilistic CV teleportation should be assessed with average quality, universality, and heralding rate treated on an equal footing.

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• Quantum information processing with continuous variables
• Quantum optics
• Quantum teleportation