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We present constraints on the amplitude of local Primordial Non-Gaussianities(PNG), $f_{\rm NL}$, using the quasar sample in the Sloan Digital Sky Survey IVextended Baryon Oscillation Spectroscopic Survey Data Release 16. We analyzethe power spectrum monopole, testing for the presence of scale dependent galaxybias induced by local PNG. Our analysis makes use of optimal redshift weightsthat maximize the response of the quasar sample to the possible presence of nonzero PNG. We find $-4<f_{\rm NL}<27$ at $68\%$ confidence level, which is amongthe strongest bounds with Large Scale Structure data. The optimal analysisreduces the error bar by about 10% compared to the standard one, an amountwhich is smaller than what was expected from a Fisher matrix analysis. This,and the reduced improvement over previous releases of the same catalog, suggestthe presence of still unknown systematic effects in the data. If the quasarshave a lower response to local PNG, our optimal constraint becomes $-23<f_{\rmNL}<21$ at $68\%$, with an improvement of $30\%$ over standard analyses. Wealso show how to use the optimal weights to put data-driven priors on thesample's response to local PNG.

Optimal constraints on Primordial non-Gaussianity with the eBOSS DR16 quasars in Fourier space