Sequential product on standard effect algebra $\mathcal{E}(H)$

Abstract

A quantum effect is an operator $A$ on a complex Hilbert space $H$ that satisfies $0\le A\le I$, $\mathcal{E}(H)$ is the set of all quantum effects on $H$. In 2001, Professor Gudder and Nagy studied the sequential product $A\circ B=A^{1/2}B{A}^{1/2}$ of $A,B\in \mathcal{E}(H)$. In 2005, Professor Gudder asked: Is $A\circ B=A^{1/2}B{A}^{1/2}$ the only sequential product on $\mathcal{E}(H)$? Recently, Liu and Wu presented an example to show that the answer is negative. In this paper, firstly, we characterize some algebraic properties of the abstract sequential product on $\mathcal{E}(H)$; secondly, we present a general method for constructing sequential products on $\mathcal{E}(H)$; finally, we study some properties of the sequential products constructed by the method

References in corpus (4)

• Characterization of the Sequential Product on Quantum Effects
• States on sharply dominating effect algebras
• The Uniqueness Problem of Sequence Product on Operator Effect Algebra $\epsilon (H)$
• Not each sequential effect algebra is sharply dominating

Cited by in corpus (2)

• The three types of normal sequential effect algebras
• The n-th root of sequential effect algebras