High-dimensional two-photon quantum controlled phase-flip gate

High-dimensional quantum systems have been used to reveal interesting fundamental physics and to improve information capacity and noise resilience in quantum information processing. However, it remains a significant challenge to realize universal two-photon quantum gates in high dimensions with high success probability. Here, by considering an ion-cavity QED system, we theoretically propose, to the best of our knowledge, the first high-dimensional, deterministic, and universal two-photon quantum gate. By using an optical cavity embedded with a single trapped <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mmultiscripts><a:mi>Ca</a:mi><a:none/><a:mo>+</a:mo><a:mprescripts/><a:none/><a:mn>40</a:mn></a:mmultiscripts></a:math> ion, we achieve a high average fidelity larger than 98% for a quantum controlled phase-flip gate in four-dimensional space, spanned by photonic spin angular momenta and orbital angular momenta. Our proposed system can be an essential building block for high-dimensional quantum information processing, and also provides a platform for studying high-dimensional cavity QED. Published by the American Physical Society 2024