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IQI Weekly Seminar

Tuesday, August 23, 2016
3:00pm to 4:00pm
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Annenberg 213
Multivariate trace inequalities
David Sutter, ETH Zurich,
  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).
For more information, please contact Jackie O'Sullivan by phone at 626.395.4964 or by email at [email protected].