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Register a new userHigh-dimensional quantum gates using full-field spatial modes of photons
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Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g. wave plates for polarisation. However for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations when the number of phase modulation planes is comparable to the number of modes. More importantly, we experimentally implement several high-dimensional quantum gates for up to 5-dimensional states encoded in the full-field mode structure of photons. In particular, we realise cyclic and quantum Fourier transformations, known as Pauli $hat{X}$-gates and Hadamard $hat{H}$-gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect unitarity by means of quantum process tomography unveiling a process purity of 99%. Lastly, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e. azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation and sensing schemes.
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A simple and flexible scheme for high-dimensional linear quantum operations on optical transverse spatial modes is demonstrated. The quantum Fourier transformation (QFT) and quantum state tomography (QST) via symmetric informationally complete positive operator-valued measures (SIC POVMs) are implemented with dimensionality of 15. The matrix fidelity of QFT is 0.85, while the statistical fidelity of SIC POVMs and fidelity of QST are ~0.97 and up to 0.853, respectively. We believe that our device has the potential for further exploration of high-dimensional spatial entanglement provided by spontaneous parametric down conversion in nonlinear crystals.
An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multi-photonic quantum systems. The proposals rely on two new ideas: (I) a novel high-dimensional quantum non-demolition measurement, (II) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world, and identify important pathways for experimental research in the near future. The concept has been found using the computer algorithm Melvin for designing computer-inspired quantum experiments. This demonstrates that computer algorithms can inspire new ideas in science, which is a widely unexplored potential.
Quantum key distribution (QKD) promises information-theoretically secure communication, and is already on the verge of commercialization. Thus far, different QKD protocols have been proposed theoretically and implemented experimentally [1, 2]. The next step will be to implement high-dimensional protocols in order to improve noise resistance and increase the data rate [3-7]. Hitherto, no experimental verification of high-dimensional QKD in the single-photon regime has been conducted outside of the laboratory. Here, we report the realization of such a single-photon QKD system in a turbulent free-space link of 0.3 km over the city of Ottawa, taking advantage of both the spin and orbital angular momentum photonic degrees of freedom. This combination of optical angular momenta allows us to create a 4-dimensional state [8]; wherein, using a high-dimensional BB84 protocol [3, 4], a quantum bit error rate of 11% was attained with a corresponding secret key rate of 0.65 bits per sifted photon. While an error rate of 5% with a secret key rate of 0.43 bits per sifted photon is achieved for the case of 2-dimensional structured photons. Even through moderate turbulence without active wavefront correction, it is possible to securely transmit information carried by structured photons, opening the way for intra-city high-dimensional quantum communications under realistic conditions.
High-dimensional entangled photons are a key resource for advanced quantum information processing. Efficient processing of high-dimensional entangled photons requires the ability to synthesize their state using general unitary transformations. The leading technology for processing photons in high-dimensions is integrated multiport interferometers. However, such devices are incompatible with free-space and fiber-based systems, and their architecture poses significant scaling challenges. Here we unlock these limitations by demonstrating a reconfigurable processor of entangled photons that is based on multi-plane light conversion (MPLC), a technology that was recently developed for multiplexing hundreds of spatial modes for classical free-space and fiber communication. To demonstrate the flexibility of MPLC, we perform four key tasks of quantum information processing using the same MPLC hardware: entanglement certification, tailored two-photon interference, arbitrary state transformations, and mode conversion. Based on the high degree of control we obtain, we expect MPLC will become a leading platform for future quantum technologies.
Spatial modes of light constitute valuable resources for a variety of quantum technologies ranging from quantum communication and quantum imaging to remote sensing. Nevertheless, their vulnerabilities to phase distortions, induced by random media, impose significant limitations on the realistic implementation of numerous quantum-photonic technologies. Unfortunately, this problem is exacerbated at the single-photon level. Over the last two decades, this challenging problem has been tackled through conventional schemes that utilize optical nonlinearities, quantum correlations, and adaptive optics. In this article, we exploit the self-learning and self-evolving features of artificial neural networks to correct the complex spatial profile of distorted Laguerre-Gaussian modes at the single-photon level. Furthermore, we demonstrate the possibility of boosting the performance of an optical communication protocol through the spatial mode correction of single photons using machine learning. Our results have important implications for real-time turbulence correction of structured photons and single-photon images.
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