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

TL;DR

This paper introduces a novel method for quantum state tomography of single-photon hyperentangled states across multiple degrees of freedom using a single intensity measurement, simplifying experimental procedures.

Contribution

It proposes a framework that encodes quantum information into spatial degrees of freedom, enabling full state reconstruction with a single measurement and extending to multiphoton states.

Findings

Numerical demonstration with OAM-spin and OAM-frequency entangled states.

Method reduces measurement complexity and acquisition time.

Enables detection of DOFs like polarization with simple cameras.

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.