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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
  • others
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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.

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Two perspectives:

  • Yes. Schrödinger's equation is just the continuous time version of unitary evolution. Thus, if you take unitary evolution from quantum information and ask to make it continuous, you arrive at the Schrödinger equation.

  • No. There is neither continuous time in quantum information (depends on your "definition" of quantum information), nor is there $\hbar$. Thus, you cannot arrive at the Schrödinger equation.

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  • $\begingroup$ So, we can get to the form of the SE because it is the differential equation that results in unitary evolution. Once we have the form of the equation, we have to interpret the "$H$" that is multiplying the wave function as total energy. I take it that can be at least started by inserting a plane wave solution for the wave function $\psi$, noticing that $-i\hslash d\psi /dt=\hslash\omega\psi$ (for now ignore how $\hslash$ got there) and we know that kinetic energy of a quantum object is ℏω, so, in the case of no potential, $H$ is KE, and so infer that, in general, $H$ should be total E? $\endgroup$ – user3536736 Aug 8 '19 at 4:13
  • $\begingroup$ You won't get the interpretation of $H$ from quantum information. $\endgroup$ – Norbert Schuch Aug 8 '19 at 10:13

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