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QUANTUM thcoiy is undeniably one of the most powerful and successful theories in physics. For most of this century physicists have been using quantum theory to predict and explain the behaviour of light and matter in an amazing range of experiments and applications. From high-energy collisions and neutron stars to semiconductors and lasers, the theory has proven itself time and time again.A central idea in quantum mechanics is the wavefunction. This contains all of the information that one can possibly know about a quantum system. However, it is only in recent years that the experimental technology and theoretical knowhow has been available to create light and/or matter in a specific quantum state and to perform measurements on it. For a researcher interested in the fundamental laws of nature, this offers fascinating possibilities for testing elementary predictions of quantum mechanics. Moreover, this ability to "engineer" quantum states is also of immense practical interest in many areas of physics and beyond. In gravitational-wave detection, for example, specifically designed quantum states will allow high-precision intcrfcrometry measurements by reducing quantum noise in experiments. And the yield of chemical reactions could be improved by preparing the reactants in specially chosen quantum states. The active control of chemical reactions on the microscopic level has great potential for industrial applications.These breakthroughs will rely on the development of accurate and dependable methods to analyse and extract experimentally the complete information characterizing the state of quantum systems. The state-of-the-art in quantum-state measurements is rapidly approaching these goals, as the experiments described in this article will illustrate.

We i n v estigate the general case of the photon distribution of a two-mode squeezed vacuum and show that the distribution of photons among the two modes depends on four parameters: two squeezing parameters, the relative phase between the two oscillators and their spatial orientation. The distribution of the total number of photons depends only on the two squeezing parameters. We derive analytical expressions and present pictures for both distributions.

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