The bosonic minimum output entropy conjecture and Lagrangian minimization
Abstract
We introduce a new form for the bosonic channel minimal output entropy conjecture, namely that among states with equal input entropy, the thermal states are the ones that have slightest increase in entropy when sent through a infinitesimal thermalizing channel. We then detail a strategy to prove the conjecture through variational techniques. This would lead to the calculation of the classical capacity of a communication channel subject to thermal noise. Our strategy detects input thermal ensembles as possible solutions for the optimal encoding of the channel, lending support to the conjecture. However, it does not seem to be able to exclude the possibility that other input ensembles can attain the channel capacity.
Cite
@article{arxiv.0906.2758,
title = {The bosonic minimum output entropy conjecture and Lagrangian minimization},
author = {S. Lloyd and V. Giovannetti and L. Maccone and N. J. Cerf and S. Guha and R. Garcia-Patron and S. Mitter and S. Pirandola and M. B. Ruskai and J. H. Shapiro and H. Yuan},
journal= {arXiv preprint arXiv:0906.2758},
year = {2010}
}
Comments
Here we detail the progress in attacking the minimum output entropy conjecture with an infinitesimal thermalizing map approach. In particular, we give the details on why we could not complete the proof of the conjecture with this strategy