Quantum Information Processing with Complex Media (Quomplex)

The worlds most advanced quantum technologies rely for a large part on the control and manipulation of quantum states of light. From entanglement swapping to Boson sampling, linear optical devices such as beam splitters and integrated photonic circuits are essential for accomplishing key tasks in quantum communication and computation. However, precisely controlling complex quantum states of light in the lab remains a challenge: current approaches are either prohibitively complex or too lossy for practical realisation. In QuompleX, we propose an alternative approach for the control and manipulation of quantum states of light. Recent years have seen the development of techniques that allow unprecedented control over classical light propagation through complex scattering media. Such media are analogous to a complex network of optical elements, control over which has led to exciting new possibilities for biomedical imaging and classical communication. Here, we aim to harness the transformative potential of complex media for quantum information processing. By carefully controlling the scattering process for multiple photons, we will use complex media as multimode linear optical networks for generating, manipulating, and transporting complex quantum states of light. In this manner, we aim to overcome the problems of control and scalability that normally plague quantum photonic networks, and push the limits of their capacity and noise- robustness. In QuompleX, we will first theoretically study light propagation through complex media such as multi-mode fibres and design computational algorithms for its control and manipulation. Then, we will apply these techniques in experiment to design high-dimensional quantum logic gates and generalised multi-mode linear networks for generating complex, multi-photon entanglement. Finally, we will use these tools to demonstrate multi-level, device-independent quantum communication protocols in complex media and implement noise-resistance tests of quantum mechanics.

Controlling an entangled state of light is an extremely demanding task in quantum optics. To manipulate even the simplest such states, entangled photons are intricately combined via a series of optical elements such as mirrors and beam splitters. As the complexity of these states is increased, the network of elements required to create them also becomes rather large. Each element in such a network must also be precisely controlled, which presents a difficult challenge to quantum physicists. When a beam of light impinges on a layer of paint or a sugar cube, it undergoes millions of reflections and transformations. Such everyday objects are surprisingly analogous to a complex network of optical elements, with the difference being that any information transmitted through them is usually lost. In recent years however, advances in technology for shaping the wavefront of light, combined with fast computational algorithms have resulted in unprecedented control over how light propagates through such disordered media. Using these techniques, scientists have achieved remarkable feats such as sending an entire image down an optical fibre the thickness of a human hair! The FWF project "QuompleX" harnesses the potential of disordered media as miniature "quantum optics laboratories" for manipulating and transporting large, complex entangled states of light. By carefully controlling the quantum states of photons entering such media, the millions of scattering events that would normally scramble their quantum information can be put to work for manipulating it instead! In this manner, complex scattering media are made to serve the same function as large networks of quantum optical elements, while overcoming the problem of control and scalability that normally plague such networks. The project focused on a specific type of scattering medium called a multi-mode fibre (MMF), which is commonly used in high-speed internet connections. The project first developed methods to efficiently measure complex quantum states of light entangled in many "dimensions" or levels, and showed that they can tolerate large amounts of noise that would normally destroy entanglement. The project then demonstrated the transport of such high-dimensional entangled states through a multi-mode fibre for the first time, opening up a pathway towards high-capacity and noise-robust quantum communication networks in the future. Finally, the project developed machine learning algorithms for the control of complex quantum states of light using quantum circuits programmed in complex scattering media, which are currently being used for manipulating entanglement in the laboratory.