Ptychography of pure quantum states

Area of Science:

• Quantum information science
• Quantum state reconstruction
• Computational imaging

Background:

• Ptychography is a computational imaging technique that reconstructs an object's transmission function from diffraction intensities of overlapping illuminated regions.
• Quantum state reconstruction is crucial for understanding and utilizing quantum systems.

Purpose of the Study:

• To propose and numerically validate a quantum analogue of ptychography for reconstructing d-dimensional pure states.
• To assess the method's performance under realistic noise conditions and varying system parameters.

Main Methods:

• A quantum ptychographic scheme using n rank-r projectors to scan overlapping parts of a quantum state.
• Measurement of the moduli of d Fourier amplitudes for each projected part.
• Iterative phase retrieval algorithm, equivalent to alternating gradient search, for state estimation.

Main Results:

• Numerical simulations for d up to 100 demonstrated high-fidelity reconstructions (infidelities < 10^-2) across different scenarios (economic, costly, multiqubit).
• The method proved resilient to realistic depolarization and Poissonian noise.
• The postprocessing algorithm is simple, fast, and avoids local-minima stagnation.

Conclusions:

• Quantum ptychography offers a robust and efficient method for quantum state reconstruction.
• The technique utilizes a single measurement basis, with data diversity and redundancy provided by overlapping projections.
• The proposed scheme is applicable to various quantum systems, including multiport interferometers.