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Arithmetic with spatiotemporal optical vortex of integer and fractional topological charges

Spatiotemporal optical vortices carry transverse orbital angular momentum (t-OAM), which give rise to spatiotemporal topological charge (ST-TC). To unleash the full potential of t-OAM in expanding the capacity of communication and computing, we demonstrate the first optical information-processing pipeline capable of performing addition and subtraction on ST-TC values, regardless of whether they are integer or fractional. Additionally, we established a readout method for those mathematical operations through imaging spectral analysis, providing a robust optical basis toward arithmetic operations and verification. These new capabilities mark crucial advancements toward full arithmetic operations on the ST-TC of light for bosonic state computation and information processing.