Operational axioms for C*-algebra representation of transformations

TL;DR

This paper derives a C*-algebra framework for physical system transformations from operational postulates, analyzing quantum mechanics and discussing potential extensions to other no-signaling theories.

Contribution

It introduces a novel derivation of C*-algebra representations based on operational postulates related to independence and faithful states.

Findings

C*-algebra representation is derived from operational postulates

Quantum mechanics fits within this C*-algebra framework

Discussion on extending the framework to other no-signaling theories

Abstract

It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states. Both notions are crucial for the possibility of performing experiments on the system, in preventing remote instantaneous influences and in allowing calibration of apparatuses. The case of Quantum Mechanics is thoroughly analyzed. The possibility that other no-signaling theories admit a C*-algebra formulation is discussed.