I know that some people think that quantum information theory/science is fundamental physics. I also know that there are many definitions, theorems and rules in the field of quantum information. They include:
- the most fundamental unit of quantum information is the qubit, a Hilbert Space vector that is a superposition of two basis states
- qubit basis states can also be combined to form product basis states
- quantum states evolve via unitary transformation
- no broadcast theorem
- no-clone theorem
- no-delete theorem
- no-teleportation theorem (qubit probability amplitudes cannot be read)
- no-communication theorem
- no-hiding theorem
- teleportation of qubits no faster than c theorem
- nature of entanglement of qubits
- definition of Von Neumann Entropy
Many of those are derived with Schrodinger's equation assumed in the proof. However, if we take these definitions, theorems, etc. as axioms, of sorts, can we derive Schrodinger's equation and thereby show that quantum information theory can be thought of as fundamental physics? I imagine that there is an inelegant, obvious, brute-force way to do so, but I am wondering if anyone has discovered a minimum set of quantum information statements from which schrodinger's equation can be derived.
I did look to see if this was answered and did not see one, so I apologize if I missed something already posted.