Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps
Abstract
Squashed entanglement [Christandl and Winter, J. Math. Phys. 45(3):829-840 (2004)] is a monogamous entanglement measure, which implies that highly extendible states have small value of the squashed entanglement. Here, invoking a recent inequality for the quantum conditional mutual information [Fawzi and Renner, Commun. Math. Phys. 340(2):575-611 (2015)] greatly extended and simplified in various work since, we show the converse, that a small value of squashed entanglement implies that the state is close to a highly extendible state. As a corollary, we establish an alternative proof of the faithfulness of squashed entanglement [Brandao, Christandl and Yard, Commun. Math. Phys. 306:805-830 (2011)]. We briefly discuss the previous and subsequent history of the Fawzi-Renner bound and related conjectures, and close by advertising a potentially far-reaching generalization to universal and functorial recovery maps for the monotonicity of the relative entropy.
Keywords
Cite
@article{arxiv.1410.4184,
title = {Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps},
author = {Ke Li and Andreas Winter},
journal= {arXiv preprint arXiv:1410.4184},
year = {2020}
}
Comments
14 pages, Springer journal style. In v2 we have removed the claim about multi-party squashed entanglement (see new Appendix B for why) and corrected other smaller mistakes; v3 takes into account the developments since the original posting and has a new structure; v4 final accepted version