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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Path-Transverse Electric Mode Hyperentanglement on an Integrated Photonic Chip

Imogen Forbes, Patrick Yard, Martin Bielak, Matthew Jones, M K Thomas, Stefano Paesani, Massimo Borghi, Anthony Laing

Published Jun 23, 2025• 0 citations
Publisher

Abstract

Hyperentanglement, or the simultaneous entanglement of qubits across multiple degrees of freedom (DOFs), in-creases the dimensionality of the Hilbert space whilst maintaining particle number [1]. This increase in dimension allows the state to carry more information than a state entangled in a single DOF, which offers benefits in quantum protocols such as superdense coding and long-distance communication [2].

DOI
10.1109/cleo/europe-eqec65582.2025.11110386

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Hyperentanglement, or the simultaneous entanglement of qubits across multiple degrees of freedom (DOFs), in-creases the dimensionality of the Hilbert space whilst maintaining particle number [1]. This increase in dimension allows the state to carry more information than a state entangled in a single DOF, which offers benefits in quantum protocols such as superdense coding and long-distance communication [2].
Multidimensional entangled photon states represent a useful resource for large-scale quantum communication networks. By leveraging multiple degrees of freedom (DoFs) of photons, the dimensionality of the Hilbert space can be expanded without increasing the number of particles, enhancing the efficiency of quantum information processing. Specifically, hyperentanglement, i.e. simultaneous entanglement across multiple DoFs, is robust against decoherence, thus providing strengthened performance in noisy quantum communication protocols with respect to n-photon quantum states [1].
Encoding many qubits in different degrees of freedom (DOFs) of single photons is one of the routes toward enlarging the Hilbert space spanned by a photonic quantum state. Hyperentangled photon states (that is, states showing entanglement in multiple DOFs) have demonstrated significant implications for both fundamental physics tests and quantum communication and computation. Increasing the number of qubits of photonic experiments requires miniaturization and integration of the basic elements, and functions to guarantee the setup stability, which motivates the development of technologies allowing the precise control of different photonic DOFs on a chip. We demonstrate the contextual use of path and polarization qubits propagating within an integrated quantum circuit. We tested the properties of four-qubit linear cluster states built on both DOFs, and we exploited them to perform the Grover's search algorithm according to the one-way quantum computation model. Our results pave the way toward the full integration on a chip of hybrid multi-qubit multiphoton states. Integrated optical chips performing operations with ‘hyperentangled photons’ have been fabricated by a team in Italy. Hyperentanglement, in which a photon is simultaneously entangled in several different degrees of freedom, is attracting interest because it offers a means to encode more than one quantum bit of information (qubit) onto the same photon, thus increasing the efficiency of quantum computation. However, for the approach to be practical, the hardware needed for hyperentanglement should ideally be an integrated chip platform. Professor Paolo Mataloni and co-workers have done just that using a chip that features high-quality optical waveguides written in a glass by a femtosecond laser. Their chip was used to engineer a four-qubit cluster state via hyperentanglement of the paths and polarizations of two photons. The researchers tested this cluster state by successfully performing Grover’s search algorithm.
Hybrid encodings, where multiple degrees of freedom are used to encode quantum information, can increase the size of the Hilbert space with minimal increase to hardware requirements. We show a reprogrammable integrated photonic device, with multimodal components designed to allow for control over the transverse electric modes. We use this device to generate qudit states entangled in the path and transverse electric mode degrees of freedom. We generate and verify a hyperentangled state with a fidelity of F HE =67.3±0.2% and a GHZ 4 -style state with a fidelity of F GHZ 4 =85.2±0.4%. We use our hyperentangled state in a single-copy entanglement distillation protocol on-chip, highlighting how this can be used to overcome inherent hardware noise with our hyperentangled state. We also classically simulate the application of probabilistic bit flip errors within this protocol, resulting in an average 9.1% increase in the fidelity of the distilled Bell state for up to a 50% probability of bit flip error. By utilizing degrees of freedom that are readily compatible with integrated photonics, our work highlights how this hybrid encoding demonstrates a first step in using the transverse electric mode to reduce the footprint of integrated quantum photonic experiments.
Hybrid encodings, where multiple degrees of freedom are used to encode quantum information, can increase the size of the Hilbert space with minimal increase to hardware requirements. We show a reprogrammable integrated photonic device, with multimodal components designed to allow for control over the transverse electric modes. We use this device to generate qudit states entangled in the path and transverse electric mode degrees of freedom. We generate and verify a hyperentangled state with a fidelity of FHE= 67.3 +/- 0.2% and a GHZ4-style state with a fidelity of FGHZ4 = 85.2 +/- 0.4%. We use our hyperentangled state in a single-copy entanglement distillation protocol on-chip, highlighting how this can be used to overcome inherent hardware noise with our hyperentangled state. We also classically simulate the application of probabilistic bit flip errors within this protocol, resulting in an average 9.1% increase in the fidelity of the distilled Bell state for up to a 50% probability of bit flip error. By utilizing degrees of freedom that are readily compatible with integrated photonics, our work highlights how this hybrid encoding demonstrates a first step in using the transverse electric mode to reduce the footprint of integrated quantum photonic experiments. Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Encoding many qubits in different degrees of freedom (DOFs) of single photons is one of the routes towards enlarging the Hilbert space spanned by a photonic quantum state. Hyperentangled photon states (i.e. states showing entanglement in multiple DOFs) have demonstrated significant implications for both fundamental physics tests and quantum communication and computation. Increasing the number of qubits of photonic experiments requires miniaturization and integration of the basic elements and functions to guarantee the set-up stability. This motivates the development of technologies allowing the control of different photonic DOFs on a chip. Femtosecond laser writing on a glass makes possible to use both path and polarization of photon states enabling precise control of both degrees of freedom. We demonstrate the contextual use of path and polarization qubits propagating within a laser written integrated quantum circuit and use them to engineer a four qubit hyperentangled cluster state. We also characterized the cluster state and exploited it to perform the Grover's search algorithm following the one-way quantum computation model. In addition, we tested the non-local properties of the cluster state by using multipartite non-locality tests.
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.