Arbitrary unitary transformation over time-binned optical modes and the demonstration of superadditive communication

Programmable linear optical unitary transformation across many temporal modes is an enabling technology of far-reaching impact, with applications ranging from joint-detection receivers with quantum-limited communication capacity, generating temporally entangled squeezed light for quantum-enhanced photonic sensors, generating photonic cluster states for quantum computation to all-optical machine learning on native optically-encoded information. To date, implementing arbitrary temporal-mode unitary operations across N optical temporal modes usually involves a complex setup of a temporal-to-spatial mode sorter and an extensive mesh of O(N²) beamsplitters and phase shifters. Here, we present a more compact and scalable optical circuit that only iterates O(N) optical elements and O(N) time-dependent controls to perform any unitary transformation on N temporal modes on demand. We have successfully demonstrated a 16-mode optical Hadamard transform using this approach, achieving superadditive communication in photon-starved regimes. Its performance surpasses that of individual symbol-by-symbol measurements by leveraging collective quantum measurement across the 16 temporal modes.