A Hilbert Space Representation of Generalized Observables and Measurement Processes in the ESR Model

TL;DR

This paper presents a Hilbert space framework for the ESR model, reinterpreting quantum probabilities and extending the measurement process to include generalized observables within a noncontextual setting.

Contribution

It introduces a Hilbert space representation for ESR model's generalized observables and proposes a generalized projection postulate and measurement evolution.

Findings

Hilbert space representation of ESR generalized observables

A generalized projection postulate for the ESR model

A mathematical description of measurement process in ESR

Abstract

The extended semantic realism (ESR) model recently worked out by one of the authors embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the generalized observables introduced by the ESR model that satisfy a simple physical condition, propose a generalization of the projection postulate, and suggest a possible mathematical description of the measurement process in terms of evolution of the compound system made up of the measured system and the measuring apparatus.