Quantum measurement schemes related to flavor-weighted energies

TL;DR

This paper develops a density matrix framework for flavor-weighted energies in quantum systems, clarifying measurement ambiguities, linking to neutrino masses, and connecting quantum measurement schemes with cosmological neutrino energy densities.

Contribution

It introduces flavor-weighted energies within density matrix theory, relating them to measurement schemes and neutrino mass expressions, addressing ambiguities in flavor energy calculations.

Findings

Non-selective measurement scheme aligns with single-particle quantum mechanics predictions.

Flavor-weighted energies are connected to neutrino effective mass values.

Cosmological neutrino energy densities can be derived from superpositions of mass eigenstates.

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.