Geodesic
On the determination of pure quantum states by the homodyne detection
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 1, pp. 33-42

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The methods of reconstruction of the wave function of a pure state of a quantum system by quadrature distribution measured experimentally by the homodyne detection are considered. Such distribution is called optical tomogram of a state and containes one parameter $\theta$. Wave function of a state is determined exactly by its optical tomogram if last one is known for all $\theta$. But one can obtain optical tomogram from experiment of homodyne detection only for discrete number of $\theta$. We introduce some approximate methods of reconstructing the state by such information about its optical tomogram.
Keywords: quantum tomography, quantum state, density operator, wave function. 
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A. I. Dnestryan. On the determination of pure quantum states by the homodyne detection. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 1, pp. 33-42. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_1_a2/