Hi I am looking at Quantum Computation by Neilsen and Chuang at the CHSH inequality. Looking at the spin singlet state they make measurements of for example the observable Z1 and Z2-X1 and then find the expectation value of the product. I am slightly confused here because a) Z and X are gates does it just mean to find the average of the system after these have acted on the system? b)Secondly can I find the average of a two qubit system without using the density operator. If I need to use the density operator is there a simple way? Thanks (Sorry its hard to make it clear without waffling on for ages but since its a popular book hopefully someone will understand me).