Convexity of the residual entropy
Year: 2013
Type: preprint
Abstract: We consider both known and not previously studied trace functions with applications in quantum physics. By using perspectives we obtain convexity statements for different notions of residual entropy, including the entropy gain of a quantum channel as studied by Holevo and others. We give new and simplified proofs of the Carlen-Lieb theorems concerning concavity or convexity of certain trace functions by making use of the theory of operator monotone functions. We then apply these methods in a study of new types of trace functions. Keywords: Trace function, convexity, entropy gain, residual entropy, operator monotone function.
Source: arXiv (Cornell University)
Author: Frank Hansen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2808622271