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Some applications of a majorization inequality due to Bapat and Sunder. (English) Zbl 1310.15033

Summary: This paper presents applications of a remarkable majorization inequality due to R. B. Bapat and V. S. Sunder [Linear Algebra Appl. 72, 107–117 (1985; Zbl 0577.15016)] in three different areas. The first application is a proof of T. Hiroshima’s result [“Majorization criterion for distillability of a bipartite quantum state”, Phys. Rev. Lett. 91, No. 5, Article ID 057902 (2003; doi:10.1103/PhysRevLett.91.057902)] which arises in quantum information theory. The second one is an extension of some eigenvalue inequalities that have been used to bound chromatic number of graphs. The third application is a simplified proof of a majorization inequality from the analysis of distributed Kalman filtering.

MSC:

15A45 Miscellaneous inequalities involving matrices

Citations:

Zbl 0577.15016
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References:

[1] T. Ando, Majorization relations involving partial traces, private communication, 2013/2/6.
[2] Bapat, R. B.; Sunder, V. S., On majorization and Schur products, Linear Algebra Appl., 72, 107-117, (1985) · Zbl 0577.15016
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[7] Hiroshima, T., Majorization criterion for distillability of a bipartite quantum state, Phys. Rev. Lett., 91, 057902, (2003), 4 pp
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[11] Petz, D., Matrix analysis with some applications, (2011), available at
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