Sets of states and extreme points (Q1120571)

Let P be an orthoposet with a given convex set of states, \(\Delta\), on it. The author is interested in the case when the image of P under the natural embedding into the corresponding order unit normal vector space coincides with the set of extreme points of the order interval \([0,1_{\Delta}]\), where \(1_{\Delta}\) is the order unit. Several sufficient as well as necessary conditions are stated for the case, those P that are Boolean algebras are characterized, and modifications of the state space are discussed from this viewpoint.