Using one Quantum of Familiar gives you a hatching. Using up to 12 more upgrades how much xp the xp drop item gives. This forum post has spading on the basic mechanics. So, if you use more than 13 total QOFs, you'll get a new stat display on your profile, indicating how many. Example: if you had 14 QOF and used them all, your familiar's drops would give +23 xp and you'd get Unquantized Quantums: 1 on your profile.
We should probably track this with maybe like "itemLevel11681" because it affects quantized familiar experience, similar to how we track skillLevelN for upgradable skills? Mafia doesn't really do much with items that grant familiar xp right now though, the other ones like Ghost Dog Chow are commented out in modifiers.txt