Here in Ukraine, we have a nice saying: "Don't rush into the hell before your father".
I.e. don't make any prejudiced conclusions before you get any single answer.
I am too in a doubt that the OP sees the diference between OTP and SSC, but he has to answer himself.
Cryptography was my primary speciality in the university, and I know for sure that "information-theoretic security", i.e. degree of randomness, of a bit sequence, isn't a rocket science. For it to exist, the sequence must pass a row of tests. It's not so hard to achieve. Finding the actual entropy source is much harder. Without a dedicated chipset (have you ever heard of Gryada-3 (Гряда-3, roughly translated as Ridge-3) RNG module? Probably not, it's a Ukrainian invention), human interaction (mouse movement etc) or using external sensors (temperature deviations, for example) the only entropy source I can think of is RDTSC timestamp gathering.
For us mere mortals, even /dev/random will do. But the most interesting question for me is how the hell (which you shouldn't rush into before your father) the OP is going to distribute and sync the random pile of data. That alone is quite a hard problem, especially if the pile is distributed between more than two users.
So let's be patient and wait for the answers.