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Optimization of quantum divergences between unitary orbits

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Abstract

We find explicitly the extremum values of the generalized quantum Hellinger divergences, the quantum Jensen–Shannon divergences, the traces of the weighted geometric means and weighted spectral geometric means between unitary orbits. Our tools are majorization theory of eigenvalues of matrices, integral representation of Kubo–Ando means and Fiedler’s lemma.

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Acknowledgements

This research is partially funded by the Simons Foundation Grant Targeted for Institute of Mathematics, Vietnam Academy of Science and Technology. Research of the third author is partially funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the Grant Number 101.01-2020.12.

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Author notes

  1. Minh Toan Ho, Cong Trinh Le and Trung Hoa Dinh have contributed equally to this work.

Authors and Affiliations

  1. Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam

    The Khoi Vu & Minh Toan Ho

  2. Department of Mathematics and Statistics, Quy Nhon University, 170 An Duong Vuong, Quy Nhon, 55113, Vietnam

    Cong Trinh Le

  3. Department of Mathematics and Statistics, Troy University, 600 University Ave, Troy, AL, 36082, USA

    Trung Hoa Dinh

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  1. The Khoi Vu
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  2. Minh Toan Ho
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  3. Cong Trinh Le
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  4. Trung Hoa Dinh
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Correspondence to The Khoi Vu.

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Vu, T.K., Ho, M.T., Le, C.T. et al. Optimization of quantum divergences between unitary orbits. Quantum Inf Process 22, 314 (2023). https://doi.org/10.1007/s11128-023-04073-3

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