Ruminations on matrix convexity and the strong subadditivity of quantum entropy

Michael Aizenman, Giorgio Cipolloni

Research output: Contribution to journalArticlepeer-review


The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems in this field. These include convexity principles which play an essential role in the Lieb–Ruskai proof of the strong subadditivity of quantum entropy.

Original languageEnglish (US)
Article number18
JournalLetters in Mathematical Physics
Issue number1
StatePublished - Feb 2023

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • 26B25
  • 47H05
  • 81Q05
  • 82B10
  • Matrix convexity
  • Parallel sums
  • Quantum entropy
  • Strong subadditivity


Dive into the research topics of 'Ruminations on matrix convexity and the strong subadditivity of quantum entropy'. Together they form a unique fingerprint.

Cite this