RECONSTRUCTION OF QUANTUM STATES OF SPIN SYSTEMS - FROM QUANTUM BAYESIAN-INFERENCE TO QUANTUM TOMOGRAPHY

We study in detail the reconstruction of spin-1/2 states and analyze t he connection between (1) quantum Bayesian inference, (2) reconstructi on via the Jaynes principle of maximum entropy, and (3) complete recon struction schemes such asdiscrete quantum tomography. We derive an exp ression for a density operator estimated via Bayesian quantum inferenc e in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In this case the estimation corresponds to averaging over a microcanonical ensemble of pure states satisfying a set of constrain ts imposed by the measured mean values of the observables under consid eration. We show that via a ''purification'' ansatz, statistical mixtu res can also be consistently reconstructed via the quantum Bayesian in ference scheme. In this case the estimation corresponds to averaging o ver the generalized grand canonical ensemble of states satisfying the given constraints, and in the limit of large number of measurements th is density operator is equal to the generalized canonical density oper ator, which can be obtained with the help of the Jaynes principle of t he maximum entropy. We also discuss inseparability of reconstructed de nsity operators of two spins-1/2. (C) 1998 Academic Press.