some entropy arguement that came to me:

The arguements are basically based on different assumptions about the attacker's abilities to interfere with the QRNG system.

E = electronic noise;
Q = quantum noise;
T = total noise;


1, The attackers have full knowledge about the electronic noise, i.e. he/she is able to predict E at any time t;
   However, the attackers cannot tamper the values of E;
   The attackers do not have knowledge about Q;
   
   In this case:
   T = E + Q;
   H(T|E) = H(E+Q|E) = H(Q|E);
   
   Since one already knows E = e at any moment, the only uncertainty left is how much the final outcome e+q differs from e. In this case the randomness of the system is merely the entropy of random variable Q, i.e. H(Q). However, since Q cannot be measured without presence of E, one can only roughly estimate H(Q).
   
   (Doesn't seem possible to reconstruct the distribution of Q from T-E, right? subtraction of variables kind of destroyes this information...)


2, The attackers are able to control the value of the E at any time, i.e. he/she can generate a sequence of values that is completely known to him/herself and his/her co-attackers (at the output end of the RNG);
   The attackers may first observe the outcome of Q, then generate a value of E depend on its observation of Q.
   The attacker does not have knowledge about Q;

   A possible way of attack in this case:
   1, The attackers make an agreement a priori on a preselected number sequence;
   2, The attackers divide into two parties: disrupter(observe Q and control E); receiver(stay at the RNG output);
   3, The disrupter act his/her control over E such that the sequence generated, i.e. T-E, matches the pre-agreed sequence.
   4, The receiver receives the pre-agreed sequence at the output (possibly with certain errors, depends on the distribution).

   On second thought, this attack method doesn't seem reasonable: One can simply control E value to be -Q, such that Q+E is always 0, so that you don't get any randomness from the RNG...
   
   However, one can put up some restrictions to the distribution of the controlled E outcomes: the distribution of E should be the same as observed; the distribution of T should be the same as observed.