Quantum Theory from 5 reasonable axioms


Mathematical object that can be used to deter-mine the probability associated with the out-comes of any measurement that may be per-formed on a system prepared by the given preparation.

However, we do not need to measure all possible probability measurements to determine the state of a system.


  1. Probabilities
  2. Simplicity: $K = K(N)$
  3. Subspaces: If state of a system $A$ $\in M_{dim}$ subspace $\implies dim(A) = M$
  4. Composite systems: $N = N_aN_b \text{ and } K = K_aK_b$
  5. Continuity: $\exists$ a continuous reversible transformation on a system between anytwo pure states of that system