Quantum Information Processing with Spatially Structured Light

TL;DR

Problem: scale quantum information processing with photons by encoding qudits in transverse spatial modes. Approach: a top-down circuit design framework using mode-mixers to realize arbitrary unitaries $U$ in the transverse space, enabling high-dimensional local and multi-party operations. Contributions: synthesis of MPLC-, MMF-, and MCF-based implementations; demonstration of local transformations and POVMs up to $d=25$, and multi-photon interference and entanglement routing across networks with up to $300$ spatial-polarization modes. Significance: provides a scalable route to high-dimensional QIP with structured light while outlining key challenges in loss, memory, detection, and DoF interconnection that must be addressed for practical deployment.

Abstract

Qudits have proven to be a powerful resource for quantum information processing, offering enhanced channel capacities, improved robustness to noise, and highly efficient implementations of quantum algorithms. The encoding of photonic qudits in transverse-spatial degrees of freedom has emerged as a versatile tool for quantum information processing, allowing access to a vast information capacity within a single photon. In this review, we examine recent advances in quantum optical circuits with spatially structured light, focusing particularly on top-down approaches that employ complex mode-mixing transformations in free-space and fibers. In this context, we highlight circuits based on platforms such as multi-plane light conversion, complex scattering media, multimode and multi-core fibers. We discuss their applications for the manipulation and measurement of multi-dimensional and multi-mode quantum states. Furthermore, we discuss how these circuits have been employed to perform multi-party operations and multi-outcome measurements, thereby opening new avenues for scalable photonic quantum information processing.

Figures (3)

• Figure 1: Top-down design of reprogrammable circuits based on mode-mixers. Left (a,b): Circuits based on random mode-mixers such as scattering media (top) and multi-mode fibers (MMFs, bottom) can be combined with programmable phase planes to implement circuits for spatially structured light. a. Random media such as a ground glass diffuser or an MMF is used with wavefront-shaping for optical computing matthes2019optical. Any desired smaller linear operators is extracted from the large random transmission matrix by finding suitable input and output projectors. b. A spatial light modulator (SLM) is used for mapping input modes onto the spatial modes of an MMF. Orthogonal polarizations are combined with a PBS, effectively doubling the number of input channels. After the MMF, outputs can be characterized either by a single-photon (SPAD) detector or a CMOS sensor cavailles2022high. Right (c,d): Devices based on well-defined mode-mixers such as free-space propagation and multi-core fibers (MCFs). c. High-dimensional reconfigurable circuits can be built with multi-plane light converters (MPLCs), which consist of multiple, programmable phase-planes interspersed with free-space propagation kupianskyi_high-dimensional_2023. The inset depicts the simulated behaviour of a 5-plane MPLC for sorting 55 orthogonal speckle modes. The top row shows the phase masks implemented at each plane and the three following rows depict the evolution of three orthogonal speckle modes. d. The inset shows an MCF (top) that can be heated along its length and symmetrically pulled from both ends to create a multi-port beam splitter (bottom) that functions as a mode-mixer for MCF cores carine2020multi. Insets adapted from: a, Ref. matthes2019optical under OSA Open Access Agreement; b, Ref. cavailles2022high under https://opg.optica.org/content/library/portal/item/license_v2; c, Ref. kupianskyi_high-dimensional_2023 under a Creative Commons License https://pubs.aip.org/aip/app/article/8/2/026101/2870744/High-dimensional-spatial-mode-sorting-and-optical; d, Ref. carine2020multi under https://opg.optica.org/content/library/portal/item/license_v2.
• Figure 2: Experimental implementations of local quantum operations for structured light.a. Experimental implementation of a high-dimemsional $\hat{X}$-gate for Laguerre-Gaussian (LG) modes in dimensions $d=3$ with a three-plane multi-plane light converter (MPLC) brandt_high-dimensional_2020. Photons are prepared using a spatial light modulator (SLM-A), manipulated by the MPLC implemented on SLM-B, and detected via single-outcome projections using SLM-C. b. Implementation of arbitrary POVMs for $d=4$ multi-core fiber (MCF) modes with a four-path interferometer between Alice and Bob martinez2023certification. Alice prepares arbitrary MCF states in $d=4$ with phase modulators and a four-core fibre beam-splitter. Bob performs projective and non-projective measurements using a four-core fiber and a seven-core fiber, respectively. c. Demonstration of spatially encoded high-dimensional QKD in a large-scale MPLC Lib:25. Pairs of spatially entangled photons from spontaneous parametric down-conversion (SPDC) are measured by two parties with a 10-plane MPLC in different mutually unbiased bases (MUBs) of pixel modes. The bottom panels show example transformations of two 25-dimensional MUBs, showing optimized MPLC phase masks and input-mode intensities across all planes. d. An MMF-based optical circuit for manipulating and measuring bipartite quantum entanglement in up to $d=7$ pixel and LG modes goel_inverse_2024. One photon from a pair of spatially entangled photons generated is sent to Alice, who makes projective measurements using SLM$_\text{3}$ and a single-mode fiber (SMF). The other photon goes to Bob, who applies a top-down programmable circuit (an MMF sandwiched between SLM$_\text{1}$ and SLM$_\text{2}$) to perform multi-outcome measurements. The inset shows a coincidence image for a 5-outcome measurement using a Fourier gate. Figure adapted from: a, Ref. brandt_high-dimensional_2020, under a http://creativecommons.org/licenses/by/4.0/ License; b, Ref. martinez2023certification under a https://arxiv.org/abs/2201.11455 License; c, Ref. Lib:25, under an https://opg.optica.org/opticaq/fulltext.cfm?uri=opticaq-3-2-182&id=569816; d, Ref. goel_inverse_2024 under a https://arxiv.org/abs/2204.00578 License.
• Figure 3: Experimental implementations of multi-party operations for structured light: a. Left: A multiple-scattering medium acts as a multi-mode linear optical network by coupling several input and output channels wolterink2016programmable. Right: A plot showing two-photon quantum interference observed by programming a beam splitter into a scattering medium consisting of a layer of white paint. b. A reconfigurable optical network with 2 input and 23 output modes implemented with a spatial light modulator (SLM) and a multi-mode fiber (MMF) used a mode-mixer, with output modes detected using with a SPAD23 camera makowski2024large. c. A reconfigurable circuit with 8 input/output modes is constructed with four programmable phase-planes and an MMF valencia2025large. The circuit is used to implement a large-scale, multi-user quantum network with reconfigurable operations for multiplexed entanglement routing, switching, and swapping. d. Two-photon interference is observed between LG modes using a 3-plane MPLC implementing generalized beam-splitters in $d=4$hiekkamaki_high-dimensional_2021. Figure adapted from: a, Ref. wolterink2016programmable with permissions from APS; b, Ref. makowski2024large under an https://opg.optica.org/opticaq/fulltext.cfm?uri=opticaq-3-2-182&id=569816; c, Ref. valencia2025large under a Creative Commons license https://arxiv.org/abs/2501.07272 with permission; d, Ref. hiekkamaki_high-dimensional_2021 with permissions from APS.