Ptychographic reconstruction of pure quantum states

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- ⌈ d / 2 ⌉ projectors. The extension of quantum ptychography for other types of photonic spatial modes is outlined.

Morphological variations to a ptychographic algorithm

“…Ptychography has benefited from several improvements and modifications, including-but not limited to-enhanced algorithms such as extended PIE (ePIE) [29,30], combination with a Hybrid Input-Output approach [31], a reciprocal approach in which the illumination beam is tilted instead of displaced on a sample, also known as Fourier ptychography [32][33][34][35][36][37], among others [38][39][40][41]. This technique and its variants have already found application in the context of optical imaging [42][43][44][45][46][47][48], X-ray microscopy [27,41,[49][50][51][52][53][54][55][56][57][58][59], electron microscopy [27,[60][61][62][63][64][65], optical encryption [66][67][68], and recent demonstrations show promising applications in Quantum Information Science [69][70]…”