Let's say I have $k$ distributions, where $k$ is polynomially large, $D_1, D_2, \ldots, D_k$ such that each $D_i$ is computationally indistinguishable from the uniform distribution.
Is it true that the distribution $D_1 D_2 \ldots D_k$ is also computationally indistinguishable from $k$ copies of the uniform distribution?
This trivially holds if each $D_i$ is efficiently samplable. But let's say they are not.
Does the fact still remain true, by some clever way to bypass the samplability requirement?