Ptychographic reconstruction of pure quantum states.

The quantum analogue of ptychography, a powerful coherent diffractive imaging technique, is a simple method for reconstructing -dimensional pure states. It relies on measuring partially overlapping parts of the input state in a single orthonormal basis and feeding the outcomes to an iterative phase retrieval algorithm for postprocessing. We provide a proof of concept demonstration of this method by determining pure states given by superpositions of transverse spatial modes of an optical field. A set of rank- projectors, diagonal in the spatial mode basis, is used to generate partially overlapping parts of the input, and each part is projectively measured in the Fourier transformed basis. For up to 32, we successfully reconstructed hundreds of random states using =5 and = rank-⌈/2⌉ projectors. The extension of quantum ptychography for other types of photonic spatial modes is outlined.