Ptychographic reconstruction of pure quantum states

TL;DR

This paper introduces a quantum ptychography method for reconstructing pure quantum states using optical spatial modes, demonstrating successful state recovery for dimensions up to 32 with a minimal number of measurements.

Contribution

It presents the first proof of concept for quantum ptychography, enabling efficient reconstruction of high-dimensional pure states with partially overlapping measurements.

Findings

Successfully reconstructed hundreds of states up to dimension 32

Used as few as 5 measurements for certain reconstructions

Extended the method to other photonic spatial modes

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.