Quantum-like representation algorithm for trichotomous observables

TL;DR

This paper explores representing statistical data from measurements of two trichotomous observables using complex probability amplitudes, identifying specific data conditions necessary for quantum-like representation.

Contribution

It extends quantum-like representation algorithms to trichotomous observables, revealing nonlinear constraints for data to admit such representations.

Findings

Only data satisfying certain nonlinear constraints can be represented quantum-like

The complexity increases compared to dichotomous observables case

Identifies specific conditions for quantum-like data representation

Abstract

We study the problem of representation of statistical data (of any origin) by a complex probability amplitude. This paper is devoted to representation of data collected from measurements of two trichotomous observables. The complexity of the problem eventually increased comparing to with the case of dichotomous observables. We see that only special statistical data (satisfying s number of nonlinear constraints) have the quantum--like representation.