Ptychographic reconstruction of pure quantum states

• URL: http://arxiv.org/abs/2010.15349v1
• Date: Thu, 29 Oct 2020 04:12:46 GMT
• Title: Ptychographic reconstruction of pure quantum states
• Authors: M. F. Fernandes, M. A. Sol\'is-Prosser, L. Neves
• Abstract summary: We provide a proof of concept demonstration of this method by determining pure states given by superpositions of $d$ transverse spatial modes of an optical field. For $d$ up to 32, we successfully reconstructed hundreds of random states using $n=5$ and $n=d$ rank-$lceil d/2rceil$ projectors.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum analogue of ptychography, a powerful coherent diffractive imaging technique, is a simple method for reconstructing $d$-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 $d$ transverse spatial modes of an optical field. A set of $n$ rank-$r$ projectors, diagonal in the spatial mode basis, is used to generate $n$ partially overlapping parts of the input and each part is projectively measured in the Fourier transformed basis. For $d$ up to 32, we successfully reconstructed hundreds of random states using $n=5$ and $n=d$ rank-$\lceil d/2\rceil$ projectors. The extension of quantum ptychography for other types of photonic spatial modes is outlined.

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