On multivariate trace inequalities of Sutter, Berta, and Tomamichel

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.


Published in:
Journal of Mathematical Physics, 59, 1, 012204
Year:
2018
ISSN:
0022-2488
1089-7658
Laboratories:




 Record created 2020-10-01, last modified 2020-10-01


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