Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum

Spin tomography

“…The best known quantum tomographic procedure is optical homodyne tomography [3], for the reconstruction of the density matrix ̺ r of the radiation field from the homodyne probability p(x, φ). It is based on the following formula [4] …”

Optimal filtering in fractional Fourier domains

“…Problem Statement in Discrete Time: The signal observation model is given by (27) where and are column vectors, and is the matrix characterizing the degradation process. We assume that input and output processes and noise are finite length random processes and that we know the correlation matrix of the input process and noise…”

Homodyning as Universal Detection

“…The state measurement is achieved by repeating many homodyne measurements at different phases φ with respect to the local oscillator (LO). The experimental work of the group in Eugene-Oregon [1] undoubtedly established the feasibility of the method, even though the earlier data analysis were based on a filtered procedure that affected the results with systematic errors. Later, the theoretical group in Pavia-Italy presented an exact reconstruction algorithm [2], which is the method currently adopted in actual experiments (see, for example, Refs.…”