JOINT QUASI-PROBABILITY DISTRIBUTION FOR N SPIN-1/2 SYSTEMS

A quantum system is described by a density matrix which determines the joint probabilities for simultaneous eigenstates of its observables. Since there do not exist any simultaneous eigenstates of non-commuting observables, the density matrix cannot provide any information about the joint probability of their eigenstates. The quasiprobability distributions (QPDs) constructed by using the density matrix provide a means of determining these joint probabilities. Here the QPDS for a system of N spin-1/2 are constructed and the joint probabilities for their components determined.