The pixel values of an image can be casted into a real ket of a Hilbert space using an appropriate block structured addressing. The resulting state can then be rewritten in terms of its matrix product state representation in such a way that quantum entanglement corresponds to classical correlations between different coarse-grained textures. A truncation of the MPS representation is tantamount to a compression of the original image. The resulting algorithm can be improved adding a discrete Fourier transform preprocessing and a further entropic lossless compression.
@article{arxiv.quant-ph/0510031,
title = {Image compression and entanglement},
author = {Jose I. Latorre},
journal= {arXiv preprint arXiv:quant-ph/0510031},
year = {2007}
}