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 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.