High-resolution reconstruction of wave functions from part of the Q functions using a phase retrieval method in quantum state measurements of light

A high-resolution reconstruction method of the wave function of a pure quantum state from the Q function along only several parallel lines in phase space is proposed. This method involves the synthesis of wave functions reconstructed by using a phase retrieval method from measured data of the Q function along several parallel Lines. Each of the reconstructed wave functions corresponds to a part of the frequency components of the true wave function, and the part depends on the position of the line measuring in phase space. This method improves on the resolution of reconstructed wave functions compared with those of a previous method, in which the resolution was limited by the extent of the inverse Fourier transform of the wave function for the vacuum state. Numerical simulations demonstrate the effectiveness of this method in the reconstruction from direct measurement of the Q function with unbalanced homodyne detection. (C) 2000 Elsevier Science B.V. All rights reserved.