High-Dimensional Pixel Entanglement: Efficient Generation and Certification

Natalia Herrera Valencia1, Vatshal Srivastav1, Matej Pivoluska2,3, Marcus Huber4,5, Nicolai Friis4, Will McCutcheon1, and Mehul Malik1,4

1Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh, UK
2Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia
3Institute of Computer Science, Masaryk University, Brno, Czech Republic
4Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Vienna, Austria
5Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria

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Abstract

Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying capacity via wavelength and spatial-mode division multiplexing, quantum systems based on multi-mode entanglement usually suffer from low state quality, long measurement times, and limited encoding capacity. At the same time, entanglement certification methods often rely on assumptions that compromise security. Here we show the certification of photonic high-dimensional entanglement in the transverse position-momentum degree-of-freedom with a record quality, measurement speed, and entanglement dimensionality, without making any assumptions about the state or channels. Using a tailored macro-pixel basis, precise spatial-mode measurements, and a modified entanglement witness, we demonstrate state fidelities of up to 94.4% in a 19-dimensional state-space, entanglement in up to 55 local dimensions, and an entanglement-of-formation of up to 4 ebits. Furthermore, our measurement times show an improvement of more than two orders of magnitude over previous state-of-the-art demonstrations. Our results pave the way for noise-robust quantum networks that saturate the information-carrying capacity of single photons.

Entanglement has been demonstrated using many different properties of light, such as its polarisation, path, or spatial and temporal structure. The inherently high-dimensional nature of the photonic wavefunction enables one to explore entanglement significantly beyond the qubit regime, which offers several advantages in terms of information capacity and noise-robustness. However, the generation and measurement of such large quantum-entangled states is often challenging, limited by the quality, ease, scalability, and speed of generalised measurements in space and time. Here we demonstrate high-dimensional entanglement of two photons in their localised transverse spatial position or “pixel” modes. Through the use of carefully engineered measurements and a specially designed entanglement witness, we certify high-dimensional pixel entanglement with a record dimensionality, quality, and measurement speed. Some examples of our measured states include entanglement in 55 local dimensions, state fidelities of up to 98.2%, and 100-fold improvements in measurement times. Our work has the potential to significantly advance quantum communication systems by pushing their capacity limits and resilience to noise.

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