2024/06/19 by Stan Gudder, Gudder, Stan, Teiko Heinosaari +1
Computer Science · #Advanced Algebra and Logic #FOS: Physical sciences #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2406.13775
openalex publication_date 2024/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate finite effect algebras and their classification. We show that an effect algebra with n elements has at least n-2 and at most (n-1)(n-2)/2 nontrivial defined sums. We characterize finite effect algebras with these minimal and maximal number of defined sums. The latter effect algebras are scale effect algebras (i.e., subalgebras of [0,1]), and only those. We prove that there is exactly one scale effect algebra with n elements for every integer n ≥ 2. We show that a finite effect algebra is quantum effect algebra (i.e. a subeffect algebra of the standard quantum effect algebra) if and only if it has a finite set of order-determining states. Among effect algebras with 2-6 elements, we identify all quantum effect algebras.