English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This note provides a succinct proof of a 1973 theorem of Lieb thatestablishes the concavity of a certain trace function. The development relieson a deep result from quantum information theory, the joint convexity ofquantum relative entropy, as well as a recent argument due to Carlen and Lieb.

From joint convexity of quantum relative entropy to a concavity theorem of Lieb