Quantum Lunch: Trace inequalities for arbitrary many matrices via pinching – University of Copenhagen

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QMath > Events > Quantum Lunch > w 06 Berta

Quantum Lunch: Trace inequalities for arbitrary many matrices via pinching

Speaker: Mario Berta, Caltech.

Mario will arrive in Copenhagen on Sunday February 7th and leave on Friday February 12th.

Abstract:
We prove matrix trace inequalities that extend the Golden-Thompson and the Araki-Lieb-Thirring inequality to arbitrary many matrices in a generalised form in terms of Schatten (quasi) norms. Our proof only relies on elementary information theoretic tools such as pinching. As an example application we extend Lieb and Ruskai's original proof of strong sub-additivity of quantum entropy to lower and upper bounds on the quantum conditional mutual information in terms of recoverability. Our new inequalities can also be used to derive tail bounds for sums of independent random matrices.