States of finite effect algebras

TL;DR

This paper characterizes finite effect algebras with states by constructing matrices and establishing a rank condition that determines the existence of a state.

Contribution

It introduces a novel matrix-based criterion for identifying when a finite effect algebra admits a state.

Findings

Matrices A and B are constructed for finite effect algebras.

A finite effect algebra has a state if and only if rank A equals rank B.

The rank condition provides a practical test for the existence of states.

Abstract

In this paper we characterize finite effect algebras which have a state. We construct two matrices $A$ and $B$ assigned to a finite effect algebra $E$ and show that if $E$ has a state then rank$A=$ rank$B$.