Squashed Entanglement, kExtendibility, Quantum Markov Chains, and Recovery Maps
Abstract
Squashed entanglement (Christandl and Winter in J. Math. Phys. 45(3):829840, 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 in Commun. Math. Phys. 340(2):575611, 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 (Brandão et al. Commun. Math. Phys. 306:805830, 2011). We briefly discuss the previous and subsequent history of the FawziRenner bound and related conjectures, and close by advertising a potentially farreaching generalization to universal and functorial recovery maps for the monotonicity of the relative entropy.
 Publication:

Foundations of Physics
 Pub Date:
 August 2018
 DOI:
 10.1007/s1070101801436
 arXiv:
 arXiv:1410.4184
 Bibcode:
 2018FoPh...48..910L
 Keywords:

 Entanglement;
 Quantum mutual information;
 Quantum information theory;
 Quantum Physics;
 Mathematical Physics
 EPrint:
 14 pages, Springer journal style. In v2 we have removed the claim about multiparty squashed entanglement (see new Appendix B for why) and corrected other smaller mistakes