Quantum Enhanced Phase Retrieval

TL;DR

This paper demonstrates that using quantum states of light in phase retrieval significantly improves accuracy and convergence speed over classical methods by leveraging a larger Hilbert space for constraints.

Contribution

It introduces a quantum-enhanced phase retrieval method that generalizes the Gerchberg-Saxton algorithm to quantum photon correlation measurements, showing improved results.

Findings

Quantum light yields more accurate phase reconstructions.

Quantum approach converges faster than classical algorithms.

Classical method often yields ambiguous solutions.

Abstract

The retrieval of phases from intensity measurements is a key process in many fields in science, from optical microscopy to x-ray crystallography. Here we study phase retrieval of a one-dimensional multi-phase object that is illuminated by quantum states of light. We generalize the iterative Gerchberg-Saxton algorithm to photon correlation measurements on the output plane, rather than the standard intensity measurements. We report a numerical comparison of classical and quantum phase retrieval of a small one-dimensional object of discrete phases from its far-field diffraction. While the classical algorithm was ambiguous and often converged to wrong solutions, quantum light produced a unique reconstruction with smaller errors and faster convergence. We attribute these improvements to a larger Hilbert space that constrains the algorithm.