Measuring the Quantum State of Light

Abstract

This is a well written book; it makes easy and pleasant reading for both experts and physicists working in other areas. The book is almost self-contained. It comprises six chapters. In the first three the author introduces the subject and deals with basic results and analytic tools from quantum optics: quantum theory of light and quasi-probability functions. In the fourth chapter he discusses the quantum-mechanical description of simple optical instruments. The last two chapters are the core of the book; they are devoted to a discussion of quantum tomography, joint measurement of position and momentum and the quantum-optical phase. The author was directly involved in the development of the field, which guarantees a fresh and clear exposition. At the same time he makes an open effort for a general (re)formulation of the subject and to present the `classic' solutions to a number of problems in the area. Overall, the presentation of quantum tomography is shaped by a personal view but it accounts sufficiently for the different approaches discussed in the literature. My only reservation is the way in which connections between classical and quantum tomography are presented. In particular, I find that an explicit statement that classical tomography (inverse Radon transform) cannot be straightforwardly applied to the quantum case should be made. The book was published in 1997. Since then the field has been growing rapidly and impetuously and the book shows its age. Nevertheless, it is still a useful reference tool for active researchers and a nice and valuable introduction for (graduate) students who are entering this area. It is worth noting that only a few books have been published on this subject; Leonhardt's volume is well written and to the point. The book is dedicated to Harry Paul, the supervisor of Leonhardt's postdoctoral thesis and the coauthor of most of his papers in the area. M G A Paris