The Uniqueness Problem of Sequence Product on Operator Effect Algebra $\epsilon (H)$

Abstract

A quantum effect is an operator on a complex Hilbert space $H$ that satisfies $0\le A\le I$. We denote the set of all quantum effects by $\mathcal{E}(H)$. In this paper we prove, Theorem 4.3, on the theory of sequential product on $\mathcal{E}(H)$ which shows, in fact, that there are sequential products on $\mathcal{E}(H)$ which are not of the generalized Lüders form. This result answers a Gudder's open problem negatively.

References in corpus (1)

• Characterization of the Sequential Product on Quantum Effects

Cited by in corpus (7)

• Sequential product on standard effect algebra $\mathcal{E}(H)$
• Sequential Product Spaces are Jordan Algebras
• A universal property for sequential measurement
• Three characterisations of the sequential product
• A characterisation of ordered abstract probabilities
• The three types of normal sequential effect algebras
• The Continuity of Sequential Product of Sequential Quantum Effect Algebras