Exact Mapping from Singular Value Spectrum of a Class of Fractal Images to Entanglement Spectrum of One-Dimensional Free Fermions

We examine singular value spectrum of a class of two-dimensional fractal images. We nd that the spectra can be mapped onto entanglement spectra of free fermions in one dimension. This exact mapping tells us that the singular value decomposition is a way of detecting a holographic relation between classical and quantum systems.