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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: comp.misc
Subject: Re: Truly Random Numbers On A Quantum Computer??
Date: Fri, 28 Mar 2025 23:10:36 -0000 (UTC)
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On Fri, 28 Mar 2025 21:16:29 -0000 (UTC), I wrote:

> The definition of “randomness” is “you don’t know what’s coming next”.
> How do you prove you don’t know something? You can’t. There are various
> statistical tests for randomness, but remember that a suitably encrypted
> message can pass every one of them, and a person who knows the message
> knows that the bitstream is not truly random.

Here’s an even simpler proof, by reductio ad absurdum.

Suppose you have a sequence of numbers which is provably random. Simply 
pregenerate a large bunch of numbers according to that sequence, and store 
them. Then supply them one by one to another party. The other party 
doesn’t know what’s coming next, but you do. Therefore they are not random 
to you.

Which contradicts the original assumption of provable randomness. QED.