A generalized matrix power mean and a new quantum Hellinger divergence. (English) Zbl 07896162
Keywords:
positive definite matrices; matrix equations; weighted geometric mean; fixed point theorem; quantum divergences; Thompson metricReferences:
| [1] | Dinh, T. H.; Le, C. T.; Le, X. D.; Pham, T. C., Some matrix equations involving the weighted geometric mean, Adv. Operat. Theory, 7, 2, 2022 · Zbl 1480.15015 · doi:10.1007/s43036-021-00165-y |
| [2] | Trentelman, H. L.; van der Woude, J. W., Almost invariance and noninteracting control: A frequency-domain analysis, Linear Algebra Appl., 101, 221-254, 1988 · Zbl 0666.93035 · doi:10.1016/0024-3795(88)90152-8 |
| [3] | van der Woude, J. W., Almost non-interacting control by measurement feedback, Syst. Control Lett., 9, 7-16, 1987 · Zbl 0623.93028 · doi:10.1016/0167-6911(87)90003-X |
| [4] | Pusz, W.; Woronowicz, S. L., Functional calculus for sesquilinear forms and the purification map, Math. Phys., 8, 159-170, 1975 · Zbl 0327.46032 |
| [5] | Moakher, M., A differential geometric approach to the geometric mean of symmetric positive-definite matrices, SIAM J. Matrix Anal. Appl., 26, 735-747, 2005 · Zbl 1079.47021 · doi:10.1137/S0895479803436937 |
| [6] | Bhatia, R.; Holbrook, J., Riemannian geometry and matrix geometric means, Linear Algebra Appl., 413, 594-618, 2006 · Zbl 1088.15022 · doi:10.1016/j.laa.2005.08.025 |
| [7] | Bhatia, R.; Gaubert, S.; Jain, T., Matrix versions of the Hellinger distance, Lett. Math. Phys., 109, 1777-1804, 2019 · Zbl 1420.15016 · doi:10.1007/s11005-019-01156-0 |
| [8] | T. H. Dinh, H. B. Du, A. N. Nguyen, and T. D. Vuong, ‘‘On new quantum divergences,’’ Lin. Multilin. Algebra (2023, in press). |
| [9] | Dinh, T. H.; Le, A. V.; Le, C. T.; Phan, N. Y., The matrix Heinz mean and related divergence, Hacet. J. Math. Stat., 51, 362-372, 2022 · Zbl 1497.47032 · doi:10.15672/hujms.902879 |
| [10] | Dinh, T. H.; Le, C. T.; Vo, B. K.; Vuong, T. D., Weighted Hellinger distance and in-betweenness property, Math. Inequal. Appl., 24, 157-165, 2021 · Zbl 07354295 |
| [11] | Dinh, T. H.; Le, C. T.; Vo, B. K.; Vuong, T. D., The \(\alpha \), Lin. Algebra Appl., 624, 267-280, 2021 · Zbl 07355223 · doi:10.1016/j.laa.2021.04.007 |
| [12] | Lim, Y.; Palfia, M., Matrix power means and the Karcher mean, J. Funct. Anal., 262, 1498-1514, 2012 · Zbl 1244.15014 · doi:10.1016/j.jfa.2011.11.012 |
| [13] | Seo, Y., Operator power mean due to Lawson-Lim-Palfia for \(1<t<2\), Lin. Algebra Appl., 459, 342-356, 2014 · Zbl 1307.47014 · doi:10.1016/j.laa.2014.07.011 |
| [14] | Furuta, T., Invitation to Linear Operators, 2001, London: Taylor Francis, London · Zbl 1029.47001 · doi:10.1201/b16820 |
| [15] | E. Carlen, Trace Inequalities and Quantum Entropy, An Introduction Course (2009). http://www.mathphys.org/AZschool/material/AZ09-carlen.pdf. · Zbl 1218.81023 |
| [16] | M. M. Wolf, Quantum Channels and Operations: Guided Tour (2012). http://www-m5.ma.tum.de/foswiki/pub/M5/Allgemeines/MichaelWolf/QChannelLecture.pdf. |
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