We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering strength. Compared to pseudospectral time-domain simulations, our modified Born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1, 2, and 3-dimensional systems.

The ability to implement reconfigurable linear optical circuits is a fundamental building block for the implementation of scalable quantum technologies. Here, we implement such circuits in a multimode fiber by harnessing its complex mixing using wavefront shaping techniques. We program linear transformations involving spatial and polarization modes of the fiber and experimentally demonstrate their accuracy and robustness using two-photon quantum states. In particular, we illustrate the reconfigurability of our platform by emulating a tunable coherent absorption experiment, where output probabilities of single-and two-photon survivals can be controlled. By demonstrating complex, reprogrammable, reliable, linear transformations, with the potential to scale, our results highlight the potential of complex media driven by wavefront shaping for quantum information processing.

No abstract

No abstract

It is well known that photons can carry a spatial structure akin to a ‘twisted’ or ‘rippled’ wavefront. Such structured light fields have sparked significant interest in both classical and quantum physics, with applications ranging from dense communications to light–matter interaction. Harnessing the full advantage of transverse spatial photonic encoding using the Laguerre–Gaussian (LG) basis in the quantum domain requires control over both the azimuthal (twisted) and radial (rippled) components of photons. However, precise measurement of the radial photonic degree-of-freedom has proven to be experimentally challenging primarily due to its transverse amplitude structure. Here we demonstrate the generation and certification of full-field LG entanglement between photons pairs generated by spontaneous parametric down conversion in the telecom regime. By precisely tuning the optical system parameters for state generation and collection, and adopting recently developed techniques for precise spatial mode measurement, we are able to certify fidelities up to 85% and entanglement dimensionalities up to 26 in a 43-dimensional radial and azimuthal LG mode space. Furthermore, we study two-photon quantum correlations between nine LG mode groups, demonstrating a correlation structure related to mode group order and inter-modal cross-talk. In addition, we show how the noise-robustness of high-dimensional entanglement certification can be significantly increased by using measurements in multiple LG mutually unbiased bases. Our work demonstrates the potential offered by the full spatial structure of the two-photon field for enhancing technologies for quantum information processing and communication.

No abstract

Programmable optical circuits form a key part of quantum technologies today, ranging from transceivers for quantum communication to integrated photonic chips for quantum information processing. As the size of such circuits is increased, maintaining precise control over every individual component becomes challenging, leading to a reduction in the quality of the operations performed. In parallel, minor imperfections in circuit fabrication are amplified in this regime, dramatically inhibiting their performance. Here we show how embedding an optical circuit in the higher-dimensional space of a large, ambient mode-mixer using inverse-design techniques allows us to forgo control over each individual circuit element, while retaining a high degree of programmability over the circuit. Using this approach, we implement high-dimensional linear optical circuits within a complex scattering medium consisting of a commercial multi-mode fibre placed between two controllable phase planes. We employ these circuits to manipulate high-dimensional spatial-mode entanglement in up to seven dimensions, demonstrating their application as fully programmable quantum gates. Furthermore, we show how their programmability allows us to turn the multi-mode fibre itself into a generalised multi-outcome measurement device, allowing us to both transport and certify entanglement within the transmission channel. Finally, we discuss the scalability of our approach, numerically showing how a high circuit fidelity can be achieved with a low circuit depth by harnessing the resource of a high-dimensional mode-mixer. Our work serves as an alternative yet powerful approach for realising precise control over high-dimensional quantum states of light, with clear applications in next-generation quantum communication and computing technologies.

No abstract