If two two observables are free, you can find the joint distribution of these two observables. But, by Heisenberg's Uncertainty Principle it is impossible unless $X$ and $Y$ are such that $XY=YX$.

There is any physical significance of free independence? What's the physical interpretation for two observables to be free independent?

If two observables are free, you can find the joint distribution of these two observables. But, by Heisenberg's Uncertainty Principle it is impossible unless $X$ and $Y$ are such that $XY=YX$.

Is there any physical significance of free independence? What's the physical interpretation for two observables to be free independent?

If two two observables are free, you can find the joint distribution of these two observables. But, by Heisenberg's Uncertainty Principle it is impossible unless $X$ and $Y$ are such that $XY=YX$.

There is any physical significance of free independance? What's the physical interprtation for two observables to be free independant?

If two two observables are free, you can find the joint distribution of these two observables. But, by Heisenberg's Uncertainty Principle it is impossible unless $X$ and $Y$ are such that $XY=YX$.

There is any physical significance of free independence? What's the physical interpretation for two observables to be free independent?