2 Quantum Tomographic Methods

The state of a physical system is the mathematical object that provides a complete information on the system. The knowledge of the state is equivalent to know the result of any possible measurement on the system. This chapter reviews quantum state estimation for a generic quantum system by quantum tomography i.e. from the measurement of a suitable set of observables, a quorum, on repeated preparations of the system. Topics include characterization of quora, determina- tion of the expectation value of any operator (including the nondiagonal projectors needed to construct a matrix representation of the density operator), evaluation of pattern functions, effect of instrumental noise, and example of tomographic proce- dure for harmonic systems and spins.