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arXiv:2404.05616 · Physical Review Applied

Informationally complete orbital-angular-momentum tomography with intensity measurements

M. Gil de Oliveira, André L. S. Santos, Patrick Lima, Altilano Cristino Barbosa, B. Pinheiro da Silva, Sebastião Pádua, Antonio Zelaquett Khoury

Published Jul 15, 2025• 3 citations
arXivHTMLPDF

Abstract

In this work we study the tomography of the spatial structure of light. We develop a simple technique that allows one to perform the tomography over the space of fixed order modes. The technique is based on two spatially resolved intensity measurements, the second of which is performed after the light field has undergone an astigmatic transformation implemented by a tilted lens. We demonstrate that this method is informationally complete within the considered subspaces, which is experimentally verified both in the intense and the photocount regime. We also study the effect of obstructions in our ability to reconstruct the states. The work here presented is expected to help the development of characterization techniques in the field of structured light and in its application for both classical and quantum information protocols.

DOI
10.1103/48bj-bm8b

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In this work we study the tomography of the spatial structure of light. We develop a simple technique that allows one to perform the tomography over the space of fixed order modes. The technique is based on two spatially resolved intensity measurements, the second of which is performed after the light field has undergone an astigmatic transformation implemented by a tilted lens. We demonstrate that this method is informationally complete within the considered subspaces, which is experimentally verified both in the intense and the photocount regime. We also study the effect of obstructions in our ability to reconstruct the states. The work here presented is expected to help the development of characterization techniques in the field of structured light and in its application for both classical and quantum information protocols.
While measuring the orbital angular momentum state of bright light beams can be performed using imaging techniques, a full characterization at the single-photon level is challenging. For applications to quantum optics and quantum information science, such characterization is an essential capability. Here, we present a setup to perform the quantum state tomography of photonic qubits encoded in this degree of freedom. The method is based on a projective technique using spatial mode projection via fork holograms and single-mode fibers inserted into an interferometer. The alignment and calibration of the device is detailed as well as the measurement sequence to reconstruct the associated density matrix. Possible extensions to higher-dimensional spaces are discussed.
Light carrying orbital angular momentum (OAM) has many applications ranging from optical manipulation, imaging and remote sensing, and optical communications, and can be used to perform fundamental studies in quantum mechanics and quantum information. Moreover, single photons with high-order OAM allow for increasing the amount of information carried per photon in quantum communication. This thesis describes the study of methods for the preparation and detection of OAM of light in high mode order by utilizing beam shaping techniques using spatial light modulators (SLMs). The quality of the generated high-order OAM mode is limited by optical aberrations which are induced by optical elements in realistic systems and propagation through realistic channels. In order to create and characterize the OAM modes with high quality, we investigate methods for aberration detection and correction using SLMs. These beam shaping techniques for the correction of optical aberrations allow us to generate and detect light carrying OAM with mode order ranging from l = 0 to l = 8 with good quality, and to generate high-quality superpositions of OAM modes with high mode order or in high dimensions. Furthermore, we observe low crosstalk and good levels of mode discrimination between different OAM modes of light. Our experimental setup can be applied in future studies to investigate and test different protocols in quantum information with high dimensional systems, such as high dimensional quantum state tomography.
Orbital angular momentum (OAM) of light is a promising degree of freedom for quantum communication and quantum computation. However, efficient methods to transform and measure OAM modes are still not available readily. Here, we propose a method for full quantum state tomography for arbitrary OAM states of light. The key component in our scheme is the helicity sorter, a device that can sort OAM modes of a light beam based on their Helicity. We present two setups to implement the Helicity sorted, one requires O(N)\mathcal{O}(N)O(N) number of optical elements for 2N2^N2N OAM modes, and the other uses spatial light modulators and is independent of the number of OAM modes. Ours is the first method to provide the efficient and scalable full quantum state tomography of the OAM modes and can be extremely important for quantum communication and quantum computation.
Accurate reconstruction of the complex spectrum of orbital angular momentum (OAM) superposition states is crucial for their application in high-capacity optical communications and quantum information, yet existing methods are often constrained by system complexity, extensive data requirements, or incomplete information retrieval. Here, we propose and experimentally demonstrate an iterative algorithm that enables high-fidelity recovery of the complex OAM spectrum of high-dimensional superpositions from only a few sparsely sampled patterns. The method integrates the Laguerre-Gaussian (LG) modal basis as an a priori constraint, which enables the direct retrieval of spectral coefficients by circumventing intermediate field reconstruction. To validate its performance, we reconstructed a test field composed of a random superposition of 21 LG modes, achieving fidelities of 99.3% in simulation and 97.2% in experiment using only four sparse sampling patterns. This work provides an efficient and robust tool for characterizing high-dimensional structured light, with significant potential in optical communication and quantum science.
In the context of quantum information theory, the use of certain photonic degrees of freedom allows the creation of high-dimensional quantum states, called qudits, which offer advantages over qubits in applications such as communication, cryptography, and fundamental tests of quantum mechanics. In many of these applications, it is necessary to reconstruct the quantum state to be used, since it contains all the measurable properties of a physical system. Recently, a simple method for reconstructing pure quantum states, called quantum ptychography, has been proposed. It is based on projections of the input state into various partial overlapping subspaces, each one followed by a projective measurement in the Fourier basis, which is generated by the quantum Fourier transform (QFT) of the computational basis. At the end, an iterative algorithm estimates the state from the collected data. In this work, we propose to apply this method to pure states of qudits encoded in angular position and orbital angular momentum (OAM) of single photons. For this purpose, we define these qudits based on the discretization of the spatial profile of a photon in cylindrical coordinates, through an arrangement of D angular slits, and describe their representation in the OAM basis. To apply ptychography to these qudits, we show that the intermediate projections will be implemented by simple binary spatial filters, while the measurement in the Fourier basis of the post-projection states will be performed by measuring in a basis defined by D OAM modes. Finally, we demonstrate the applicability of the ptychographic method by simulating the reconstruction of angular qudits for D = 5 and D = 12, and evaluate its experimental feasibility.