Unknown Quantum States and Operations, a Bayesian View

The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In this paper, we motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: Namely a de Finetti theorem for quantum states and a de Finetti theorem for quantum operations. The quantum-state theorem, in a closely analogous fashion to the original de Finetti theorem, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an "unknown quantum state" in quantum-state tomography. Similarly, the quantum-operation theorem gives an operational definition of an "unknown quantum operation" in quantum-process tomography. These results are especially important for a Bayesian interpretation of quantum mechanics, where quantum states and (at least some) quantum operations are taken to be states of belief rather than states of nature.Comment: 37 pages, 3 figures, to appear in "Quantum Estimation Theory," edited by M.G.A. Paris and J. Rehacek (Springer-Verlag, Berlin, 2004

A near field optical image of a gold surface: a luminescence study

International audienceThis paper addresses recent experimental findings about luminescence of a gold tip in near-field interaction with a gold surface. Our electrochemically etched gold tips show a typical, intrinsic luminescence that we exploit to track the plasmon resonance modeled by a Lorentzian oscillator. Our experimental device is based on a spectrometer optically coupled to an atomic force microscope used in tuning fork mode. Our measurements provide evidence of a strong optical coupling between the tip and the surface. We demonstrate that this coupling strongly affects the luminescence (Intensity, wavelength and FHWM) as a function of the tip position in 2D maps. The fluctuation of these parameters is directly related to the plasmonic properties of the gold surface and is used to qualify the optical near field enhancement (which subsequently plays the predominant role in surface enhanced spectroscopies) with a very high spatial resolution (typically around 20 nm). We compare these findings to the independently recorded near-field scattered elastic Rayleigh signal