Every axiomatic QM formulation (for example, [0]) I have ever seen has an axiom a statistical statement, usually about observables.
Can you provide a set of axioms reproducing QM without such an axiom?
If not, then it's inherently a statistical theory.
In your example, where a single electron lands is completely governed by a probability distribution that is determined by the setup of the test.
[0] http://en.wikipedia.org/wiki/Dirac%E2%80%93von_Neumann_axiom...
Every axiomatic QM formulation (for example, [0]) I have ever seen has an axiom a statistical statement, usually about observables.
Can you provide a set of axioms reproducing QM without such an axiom?
If not, then it's inherently a statistical theory.
In your example, where a single electron lands is completely governed by a probability distribution that is determined by the setup of the test.
[0] http://en.wikipedia.org/wiki/Dirac%E2%80%93von_Neumann_axiom...