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arXiv:2510.15774 · Optica Quantum

Hybrid path-transverse electric mode qudit encoding on an integrated photonic chip

Imogen Forbes, Patrick Yard, Martin Bielak, Molly A. Thomas, Matthew S. Jones, Stefano Paesani, Massimo Borghi, Anthony Laing

Published Jun 24, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/opticaq.597128

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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 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.
Abstract Integrated entangled photon pair source is an essential resource for both fundamental investigations and practical applications of quantum information science. Currently there have been several types of entanglement, among which the transverse-mode entanglement is becoming attractive because of its unique advantages. Here, we report an on-chip transverse-mode entangled photon pair source via the spontaneous four-wave mixing processes in a multimode silicon waveguide. Transverse-mode photon pairs are verified over multiple frequency channels within a bandwidth of ~2 THz, and a maximally entangled Bell state is also produced with a net fidelity of 0.96 ± 0.01. Our entangled photon pair source is the key element for quantum photonics based on transverse-mode, and also has the possibility to extend to higher-dimensional Hilbert space. Furthermore, the transverse-mode entanglement can be converted coherently to path and polarization entanglement, which paves the way to realizing highly complex quantum photonic circuits with multiple degrees of freedom.
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.
As an important degree of freedom (d.o.f.) in photonic integrated circuits, the orthogonal transverse mode provides a promising and flexible way to increase communication capability, for both classical and quantum information processing. To construct large-scale on-chip multimode multi-d.o.f.s quantum systems, a transverse mode-encoded controlled-NOT (CNOT) gate is necessary. Here, with the help of our new transverse mode-dependent directional coupler and attenuator, we demonstrate the first multimode implementation of a 2-qubit quantum gate. The ability of the gate is demonstrated by entangling two separated transverse mode qubits with an average fidelity of 0.89±0.02 and the achievement of 10 standard deviations of violations in the quantum nonlocality verification. In addition, a fidelity of 0.82±0.01 is obtained from quantum process tomography used to completely characterize the CNOT gate. Our work paves the way for universal transverse mode-encoded quantum operations and large-scale multimode multi-d.o.f.s quantum systems.