Programmable optical circuits form a key part of quantum technologies today. As the size of such circuits is increased, maintaining precise control over every individual component becomes challenging. Here we show how embedding an optical circuit in the higher-dimensional space of a large mode-mixer allows us to forgo control over individual elements, while retaining a high degree of programmability over the circuit. Using this approach, we implement high-dimensional linear optical circuits within a commercial multi-mode fibre placed between controllable phase planes. We employ these circuits to manipulate high-dimensional entanglement in up to seven dimensions, demonstrating their application as fully programmable quantum gates. Furthermore, we show how these circuits turn the multi-mode fibre itself into a generalized multi-outcome measurement device, allowing us to both transport and certify entanglement. Finally, we show 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 realizing precise control over high-dimensional quantum states of light.
High-dimensional entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems. Beyond being of fundamental interest, this offers significant advantages for quantum information processing. The problem of certifying these stronger correlations, however, remains an important challenge. Here we theoretically formalise and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement combined with judiciously chosen local measurements can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive two-setting inequalities for certifying the presence of genuine high-dimensional steering. We report the experimental violation of these inequalities using macro-pixel photon-pair entanglement certifying genuine high-dimensional steering in dimensions up to 15.
High-dimensional entanglement of structured light offers the potential for noise-robust, high-capacity quantum communication protocols. However, the generation, measurement, and transport of high-quality entanglement presents some unique challenges. We demonstrate the generation and measurement of two-photon macro-pixel entanglement with a record dimensionality, quality, and measurement speed. We then discuss an experiment where we unscramble high-dimensional pixel entanglement through a commercial multimode fibre. In contrast with classical techniques, entanglement is also used to measure the transmission matrix of the fibre. Interestingly, we are able to regain entanglement without manipulating the fibre or the photon that entered it.
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