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arXiv:2512.22869 · Optics Express

Any DOF All at Once: Single Photon State Tomography in a Single Measurement Setup

Roey Shafran, Ron Ziv, Mordechai Segev

quant-phSubmitted Dec 28, 2025• Announced Dec 30, 2025• 1 citation• Revised Apr 29, 2026 (v3)
v1 · Dec 28, 2025v2 · Jan 1, 2026v3 · Apr 29, 2026
arXivHTMLPDF

Abstract

Photonic quantum technologies utilize various degrees of freedom (DOFs) of light, such as polarization, frequency, and spatial modes, to encode quantum information. In the effort of further improving channel capacity of quantum communication, and for increasing the complexity of available quantum operations, high-dimensional and hyperentangled states are now gaining interest. However, efficiently measuring these high dimensional states is challenging due to the large number of measurements required for reconstructing the full density matrix via quantum state tomography (QST), and the fact that each measurement requires some modification in the experimental setup. Here, we propose a framework for reconstructing the density matrix of a single-photon hyperentangled across multiple DOFs using a single intensity-measurement obtainable from traditional cameras, and discuss extensions for multiphoton hyperentangled states. Our method hinges on the spatial DOF of the photon and uses it to encode the quantum information from the other DOFs. We numerically demonstrate this method for single-photon OAM-spin and OAM-frequency entangled states using an ideal coupler and a multimode fiber, to perform the information mixing and transfer the encoding to spatial information, where it is detected using a simple camera. This technique simplifies the experimental setup and reduces acquisition time compared to traditional QST-based methods. Moreover, it allows the recovery of DOFs that conventional cameras cannot detect, such as polarization, thus eliminating the need for projection measurements.

Journal reference
Optics Express Vol. 34, Issue 10, pp. 18997-19013 (2026)
DOI
10.1364/OE.603415

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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.
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