Ptychography of pure quantum states
arXiv:1812.11366 · doi:10.1038/s41598-019-52415-y
Abstract
Ptychography is an imaging technique in which a localized illumination scans overlapping regions of an object and generates a set of diffraction intensities used to computationally reconstruct its complex-valued transmission function. We propose a quantum analogue of this technique designed to reconstruct -dimensional pure states. A set of rank- projectors "scans" overlapping parts of an input state and the moduli of the Fourier amplitudes of each part are measured. These outcomes are fed into an iterative phase retrieval algorithm that estimates the state. Using up to 100 and around , we performed numerical simulations for single systems in an economic () and a costly () scenario, as well as for multiqubit systems (). This numeric study included realistic amounts of depolarization and poissonian noise, and all scenarios yielded, in general, reconstructions with infidelities below . The method is shown, therefore, to be resilient to noise and, for any , requires a simple and fast postprocessing algorithm. We show that the algorithm is equivalent to an alternating gradient search, which ensures that it does not suffer from local-minima stagnation. Unlike traditional approaches to state reconstruction, the ptychographic scheme uses a single measurement basis; the diversity and redundancy in the measured data---key for its success---are provided by the overlapping projections. We illustrate the simplicity of this scheme with the paradigmatic multiport interferometer.
arXiv comment11 pages, 6 figures. Published version
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