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Using the quantum information picture to describe the early universe as atime dependent quantum density matrix, with time playing the role of astochastic variable, we compute the non-gaussian features in the distributionof primordial fluctuations. We use a quasi de Sitter model to compute thecorresponding quantum Fisher information function as the second derivative ofthe relative entanglement entropy for the density matrix at two differenttimes. We define the curvature fluctuations in terms of the time quantumestimator. Using standard quantum estimation theory we compute the non-gaussianfeatures in the statistical distribution of primordial fluctuations. Ourapproach is model independent and only relies on the existence of a quasi deSitter phase. We show that there are primordial non-gaussianities, both in theform of squeezed and equilateral shapes. The squeezed limit gives a value of$f_{\rm NL} \sim n_s-1$. In the equilateral limit we find that $f_{\rm NL} \sim0.03$. The equilateral non-gaussianity is due to the non-linearity ofEinstein's equation. On the other hand, the squeezed one is due to the quantumnature of clock synchronization and thus real and cannot be gauged away as aglobal curvature. We identify a new effect: {\it clock bias} which is a purequantum effect and introduces a bias in the spectral tilt and running of thepower spectrum of order $\sim 10^{-4}$, which could be potentially measurableand yield precious information on the quantum nature of the early Universe.

How Gaussian can the Sky be? Primordial Non-Gaussianity from Quantum Information