Compressed Sensing Based on Tensor Network Machine Learning

We introduce the scheme of compressed sensing based on tensor-network machine learning, which enables to compress and communicate information through the generative tensor-network states. The state Ψ is first obtained by unsupervised learning of tensor network, which characterizes the set of training images. With Ψ and a small amount of pixels from a specific image that is to be sent, one can obtain a projected state Ψ , from which the whole sent image can be reconstructed. The key problem of selecting pixels from a specific image is solved by investigating the entanglement in the state Ψ .