Sets of states and extreme points

The natural embedding of orthoposets and quantum logics, equipped with certain sets of states, into their corresponding order-unit normed vector space is investigated. Necessary (resp. sufficient) conditions are stated for the case that the image of the embedding and the extreme points of the order interval, bounded by 0 and the order unit, coincide. Modifications of the state space are discussed from this point of view and the special case of a Boolean algebra is characterized.