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The study of the Cosmic Microwave Background (CMB) lensing potential hasestablished itself by now as a robust way of probing the physics of large-scalestructure growth. The most common estimators of the lensing potential arederived under the assumption of Gaussianity of the matter distribution and inthe Born approximation of the photon diffusion. In this paper we study theperformance of quadratic estimators when applied to realistic sky mapsextracted from multiple-lens ray tracing techniques in cosmological $N$-bodysimulations. These are expected to model accurately the effects due to thenon-Gaussianity of the matter distribution induced by its nonlinearity and thedeviation from the Born approximation. We show that both these effects on theirown lead to reconstruction biases, but these tend to partially cancel eachother when both these effects are considered together. We forecast the impactof these biases on the estimation of cosmological parameters for futurehigh-sensitivity CMB experiments like CMB-S4. We find that the cold dark matterdensity, $\Omega_\textrm{cdm}$, the optical depth to reionization $\tau$, theamplitude of primordial inflationary perturbations, $A_s$ and the sum ofneutrino masses, $M_\nu$, could be biased at the 1-2$\sigma$ level, if noexternal data set is used. We also observe a reduction of the bias if externaldata like baryon acoustic oscillations (BAO) is included.

Lensing Reconstruction in Post-Born Cosmic Microwave Background Weak Lensing