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-$\lceil d/2\rceil$ projectors. The extension of quantum ptychography for other types of photonic spatial modes is outlined.

arXiv comment4 pages, 3 figures. Published version

References in corpus (15)

• On the Measurement of Qubits
• Scalable multi-particle entanglement of trapped ions
• Quantum state tomography via compressed sensing
• Generation of maximally entangled states of qudits using twin photons
• Fourier relationship between angular position and optical orbital angular momentum
• Quantum Tomography under Prior Information
• Five measurement bases determine pure quantum states on any dimension
• Experimental minimum-error quantum-state discrimination in high dimensions
• Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator
• Efficient Pure State Quantum Tomography from Five Orthonormal Bases
• Determination of any pure spatial qudits from a minimum number of measurements by phase stepping interferometry
• Optimized generation of spatial qudits by using a pure phase spatial light modulator
• A set of $4d-3$ observables to determine any pure qudit state
• State determination: an iterative algorithm
• Ptychography of pure quantum states

Cited by in corpus (2)

• Morphological variations to a ptychographic algorithm
• Ptychographic estimation of pure multiqubit states in a quantum device