Does a reverse-biased P-N junction create quantum noise?
The noise that is created is truly random as it is generated by recombination of electrons with the atoms on the other side of the junction. The mean power density (RMS) can be calculated using the following formula:

$$i_n = \sqrt{2 I q \Delta B}$$

where \$q\$ is the electron charge, \$I\$ is the current that runs through the diode and \$\Delta B\$ is the bandwidth of the detector that measures the noise.

Apart from that, it is a stochastic process and therefore random. Read more about it here:

http://en.wikipedia.org/wiki/Noise_(electronic)#Shot_noise