Quality assessment of quantum teleportation through the distribution of fidelity
Phys. Rev. Applied 25, 064047 – Published 11 June, 2026
DOI: https://doi.org/10.1103/3gvb-qqx1
Abstract
In this work, we introduce a comprehensive statistical framework for assessing single-qubit quantum teleportation performance beyond the conventional average-fidelity benchmark. First, we derive a closed-form expression for the full probability density function of actual teleportation fidelities and apply it to both classical “measurement-and-prepare” schemes and standard quantum teleportation, considering two relevant noise models: Bell-diagonal resource states and local amplitude-damping channels. The results reveal that protocols with identical average fidelities can exhibit markedly different statistical behaviors, and that relying solely on average fidelity can mask inherent asymmetries introduced by local noise, potentially leading to spurious conclusions about symmetry. Second, we introduce a certification method based on prior importance functions (e.g., beta distributions), which unifies moment-based criteria and threshold-based success probabilities into a single figure of merit. Applying this framework, we see that certifying high-fidelity teleportation requires increasingly stronger entanglement or nonlocality, and we show that the “fighting noise with noise” effect is a feature specific to the first statistical moment (average fidelity), which masks the asymmetric degradation of local marginals, and vanishes for higher-order criteria. Our approach thus provides versatile tools for tailored, application-specific teleportation benchmarks.
