The extended phase space: a formalism for the study of quantum noise and quantum correlations

Extended Wigner and extended Weyl functions which are quartic functions of the wavefunction are introduced and their properties are studied. They provide an insight into the connection between quantum noise and quantum correlations. The general theory is applied to the examples of coherent states and thermal states. The construction of the extended Wi,oner function from quantum tomography experiments is also discussed and exemplified for the cases of superposition and also for a mixture of two coherent states.