On quantum randomness, the longest weather predictions and perfect macroscopic caos 
*

*Which is the maximum number of days we can predict future weather conditions with a reasonable degree of accuracy if we knew all of the initial conditions of everything that effects the weather down to the quantum level and with the minimal uncertainty allowed?

*Would this huge increment in precision yield significant results?

*How close are we to achieving that goal?


The goal that is set is relevant as everyone can assume that there's no point in investing more efforts to further improve in that area.
Note: though this question is very broad as it considers a lot of different climates and weather patterns it should still be possible to focus on some standard weather situation in terms of unpredictability.
 A: I'll take your statement "down to the quantum level and with the minimal uncertainty allowed" to mean that we can know the quantum state. If, as you ask in your comment " At which point in time $t_0$ [is] the probability $p_s$ for successfully predicting some macroscopic event $E$ is lower than some fixed value $p_0$?", then the short answer is we so far simply do not know. You're probing there the field of Quantum Chaos which is very much a new, highly nontrivial field. The basic problem here is that linearity is a fundamental tenet of quantum mechanics, yet linear operators and functions do not show the behaviour of Topological Transitivity (See the "Topological Mixing" heading under the Mixing(Mathematics) Wikipedia page) and other behaviours that make some classical, nonlinear systems behave chaotically. So we are yet  to agree on the mechanisms of quantum chaos, let alone give quantitative error bounds.
The article "A Prime Case of Chaos" published by the American Mathematical Society describes a fascinating possibility for the mechanisms behind quantum chaos whereby the zeros of the Zeta function become highly relevant. (These zeros were conjectured by Riemann to all lie on the line $\mathrm{Re}(z)=\frac{1}{2}$ but this conjecture - the famous Riemann Hypothesis - has never been proven).
