Characterization of quantum states in predicative logic

TL;DR

This paper introduces a logical framework using predicative logic to characterize quantum states, distinguishing pure and mixed states through the use of first order variables and random variables.

Contribution

It develops a novel logical approach to quantum states, defining pure and mixed states within a formal logical setting using random first order domains.

Findings

Pure states characterized by focusing condition

Mixed states described in propositional logic

Role of first order variables linked to contextuality

Abstract

We develop a characterization of quantum states by means of first order variables and random variables, within a predicative logic with equality, in the framework of basic logic and its definitory equations. We introduce the notion of random first order domain and find a characterization of pure states in predicative logic and mixed states in propositional logic, due to a focusing condition. We discuss the role of first order variables and the related contextuality, in terms of sequents.