i think she knew the deep magic by being present when Narnia was first created, when Aslan sang it to life. that was the beginning of Narnia, as you know. the thing is, it was mentioned in LWW about deep magic from the dawn of time which is obviously reffering to the time when Narnia was created and brought to life, and deeper magic from before the dawn of timewhich is reffered to by Aslan as deep magic to the time before Narnia was created, and that is why Aslan came to life from the stone table.
because she was present at that time, Jadis had acquired the rights to the deep magic, which states that she has the right to own any traitor and kill him/her or else Narnia will be overturned and perish in fire and water.