On multivariate trace inequalities of Sutter, Berta, and Tomamichel
- Creators
- Lemm, Marius
Abstract
We consider a family of multivariate trace inequalities recently derived by Sutter, Berta, and Tomamichel. These inequalities generalize the Golden-Thompson inequality and Lieb's triple matrix inequality to an arbitrary number of matrices in a way that features complex matrix powers (i.e., certain unitaries). We show that their inequalities can be rewritten as an n-matrix generalization of Lieb's original triple matrix inequality. The complex matrix powers are replaced by resolvents and appropriate maximally entangled states. We expect that the technically advantageous properties of resolvents, in particular for perturbation theory, can be of use in applications of the n-matrix inequalities, e.g., for analyzing the performance of the rotated Petz recovery map in quantum information theory and for removing the unitaries altogether.
Additional Information
© 2018 American Institute of Physics. Received 21 August 2017; accepted 27 November 2017; published online 23 January 2018. The author is grateful to Elliott H. Lieb for raising the question addressed in this paper. It is a pleasure to thank him as well as Mario Berta, Eric Carlen, Rupert L. Frank, and David Sutter for helpful remarks.Attached Files
Published - 1.5001009.pdf
Submitted - 1708.04836.pdf
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Additional details
- Eprint ID
- 84598
- Resolver ID
- CaltechAUTHORS:20180131-105909535
- Created
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2018-01-31Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field