Quantum measurement schemes related to flavor-weighted energies

Abstract

Reporting about the density matrix theory for a composite quantum system of flavor eigenstates, we introduce the idea of flavor-weighted energies. It provides us with the right correlation between the energies of flavor eigenstates and their measurement probabilities. In addition, the apparent ambiguities which follow from computing flavor-averaged energies are suppressed. The framework of the generalized theory of quantum measurement also provides some theoretical tools for computing the von-Neumann entropy correlated to flavor associated energies. It allows for relating flavor weighted(averaged) energies to non-selective (selective) quantum measurement schemes. As a final issue, the connection of such flavor associated energies with the expressions for neutrino effective mass values is investigated. It is straightforwardly verified that cosmological background neutrino energy densities could be obtained from the coherent superposition of mass eigenstates. Our results show that the non-selective measurement scheme for obtaining flavor-weighted energies is consistent with the predictions from the single-particle quantum mechanics.