The quantum-advantage resource in multimode OPA light: Identification, optimization, extraction

We introduce the notion and reveal remarkable properties of quantum complexity resource contained in a mixed multimode Gaussian state and providing universal quantitative characterization of its quantum advantage. The notion is based on convex optimization, multimode photon number statistics, Hafnian Master Theorem, and #P-hard complexity. We consider pulsed OPAs targeting maximal quantum complexity resource and thousands of multipartite-entangled squeezed modes of output light via nonlinear, spatio-temporally nonadiabatic generation inside OPA and optimized extraction out of OPA. We show that such figure of merit is more realistic than Bloch–Messiah supermodes and guides to multimode OPAs opening new paths to important applications in quantum information science such as generation of 3D cluster states for one-way photonic quantum computing and demonstration of quantum advantage.