Ke Li's lemma for quantum hypothesis testing in general von Neumann algebras
Abstract
A lemma stated by Ke Li in [arXiv:1208.1400] has been used in e.g. [arXiv:1510.04682,arXiv:1706.04590,arXiv:1612.01464,arXiv:1308.6503,arXiv:1602.08898] for various tasks in quantum hypothesis testing, data compression with quantum side information or quantum key distribution. This lemma was originally proven in finite dimension, with a direct extension to type I von Neumann algebras. Here we show that the use of modular theory allows to give more transparent meaning to the objects constructed by the lemma, and to prove it for general von Neumann algebras. This yields immediate generalizations of e.g. [arXiv:1510.04682].
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.02177
 Bibcode:
 2020arXiv201002177P
 Keywords:

 Mathematical Physics;
 Mathematics  Operator Algebras;
 Mathematics  Statistics Theory;
 Quantum Physics
 EPrint:
 13 pages. Remarks and comments are welcome