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Maps on positive definite operators preserving the quantum χ2α-divergence

Chen, H.-Y., Geher, G. P., Liu, C.-N., Molnár, L., Virosztek, D. and Wong, N.-C. (2017) Maps on positive definite operators preserving the quantum χ2α-divergence. Letters in Mathematical Physics, 107 (12). pp. 2267-2290. ISSN 0377-9017

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To link to this item DOI: 10.1007/s11005-017-0989-0

Abstract/Summary

We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum χ2αχα2 -divergence for some α∈[0,1]α∈[0,1] . We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:73365
Publisher:Springer

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