2009/06/15 by Seth Lloyd, S. Lloyd, Lloyd, S. +30
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.0906.2758
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
openalex publication_date 2009/06/15 · arxiv created 2010/08/18 · arxiv updated 2010/08/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.