Universal approximation of multi-copy states and universal quantum lossless data compression
Quantum Physics
2011-06-24 v2
Abstract
We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been open for more than ten years. For a deeper analysis, we have solved the mini-max problem concerning `approximation error' up to the second order. Furthermore, we have applied this result to quantum lossless data compression, and have constructed a universal quantum lossless data compression.
Cite
@article{arxiv.0806.1091,
title = {Universal approximation of multi-copy states and universal quantum lossless data compression},
author = {Masahito Hayashi},
journal= {arXiv preprint arXiv:0806.1091},
year = {2011}
}