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We demonstrate how to efficiently implement extremely high-dimensionalcompressive imaging of a bi-photon probability distribution. Our method usesfast-Hadamard-transform Kronecker-based compressive sensing to acquire thejoint space distribution. We list, in detail, the operations necessary toenable fast-transform-based matrix-vector operations in the joint space toreconstruct a 16.8 million-dimensional image in less than 10 minutes. Within asubspace of that image exists a 3.2 million-dimensional bi-photon probabilitydistribution. In addition, we demonstrate how the marginal distributions canaid in the accuracy of joint space distribution reconstructions.

Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution