IQI Weekly Seminar

  Abstract:    

The Golden-Thompson (GT) and the Araki-Lieb-Thirring (ALT) inequality are powerful tools with applications ranging from statistical physics and random matrix theory to quantum information theory. We will present intuitive and transparent proofs for these inequalities based on asymptotic spectral pinching and complex interpolation theory. These proofs immediately suggest extensions of the GT and ALT inequality to arbitrarily many matrices. We will see that our extension of the GT inequality to four matrices can be used to prove remainder terms for the monotonicity of the quantum relative entropy and strong sub-additivity of the von Neumann entropy in terms of recoverability.

 

Based on joint work with Mario Berta and Marco Tomamichel (arXiv:1604.03023).