The Orthogonality of Sequential Products in Sequential Effect Algebras.

An effect algebra (EA) is an algebraic structure useful in quantum logic. A sequential effect algebra (SEA) is an EA with a sequential product additionally defined. SEAs are useful in the study of quantum measurement theory and by extension quantum computation. A paper published by Gudder in 2005 posited multiple open problems about sequential effect algebras. Among them was the following question: if a and b are elements of a sequential effect algebra, and a is orthogonal to b , is it the case that the sequential product of a and b is orthogonal to itself? In this paper, we prove his assertion. [ABSTRACT FROM AUTHOR]