Year: 2011
Type: preprint
Abstract: We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore useless as a distance measure in this case. We study basic properties of this quantity, and find interesting relationships between the TRE and the trace norm distance. We then exploit the same techniques to obtain a new and shorter proof of a lower bound on the relative Renyi entropies in terms of the trace norm distance, $\traceρ^{1-p}σ^p \ge 1-(||ρ-σ||_1)/2$.
Source: arXiv (Cornell University)
Author: Audenaert, Koenraad M. R.
Institution: Royal Holloway University of London
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949519099