Statistical Framework for Quantum Teleportation: Fidelity Analysis and Resource Optimization

This paper establishes a comprehensive statistical framework for analyzing quantum teleportation protocols under realistic noisy conditions. We develop novel mathematical tools to characterize the complete statistical distribution of teleportation fidelity, including both mean and variance, for systems experiencing decoherence and channel imperfections. Our analysis demonstrates that the teleportation fidelity follows a characteristic distribution $F\sim \mathcal{P}(F_{\mathrm{avg}},\Delta F^2)$ where the variance $\Delta F^2$ depends crucially on entanglement quality and channel noise. We derive the optimal resource allocation condition $\partial E_{\mathrm{ent}}/\partial F/\partial C_{\mathrm{classical}}/\partial F=\beta /\alpha$ that minimizes total resource consumption while achieving target fidelity. Furthermore, we introduce a Bayesian adaptive protocol that enhances robustness against noise through real-time statistical estimation. The theoretical framework is validated through numerical simulations and provides practical guidance for experimental implementations in quantum communication networks.