As per the title, I'm wondering what exactly is going on at the quantum level that makes entanglement arise - what is the precursor? The hadamard, as I know it, is just a particular set of matrix values that make up an operator. From what I understand, in physics, entanglement is a naturally arising phenomenon stemming from the otherwise would be inconsistent state of the laws of the preservation of momentum. In the case of experiments in which a particle is broken in half before a heat interaction occurs, it is said that their spin state is ambiguous until measured because momentum has to be preserved. Yet, in the moment of interaction in which the particle is struck and broken, momentum is imparted and yet not observed; so it must be distributed across the two particles. That makes sense to me. But exactly what a Hadamard operation is doing to a single electron or quantum particle to me is not clear, because if I understand the state operator correctly, it is operating on the matrix state representation over the discrete information regarding the angles of the qubit (two complex numbers).