English

All quantum expectation values as classical statistical mean values

Quantum Physics 2007-11-18 v2

Abstract

Given a physical quantum system described by a Hilbert H, for any bounded quantum observable (a bounded self-adjoint operator) T it is possible to define several ''hidden observable'' functions f:H->R associated to T and for any quantum mixed state (a density matrix) D it is possible to define several ''hidden mixed states'' (probability measures) m on H associated to D in such a way that the following equality is verified: Trace[ b(T). D] =integral[b(f(psi)).dm(psi) whatever is the continuous function b:R->R. This formula gives a general way to express any expectation value computable in a quantum theory as a classical statistical mean value.

Keywords

Cite

@article{arxiv.0706.2603,
  title  = {All quantum expectation values as classical statistical mean values},
  author = {Antonio Cassa},
  journal= {arXiv preprint arXiv:0706.2603},
  year   = {2007}
}
R2 v1 2026-06-21T08:39:30.516Z