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Maps on positive definite operators preserving the quantum \(\chi_\alpha ^2\)-divergence. (English) Zbl 06814930
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 \(\chi_\alpha ^2\)-divergence for some \(\alpha \in [0,1]\). 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.

MSC:
47B49 Transformers, preservers (linear operators on spaces of linear operators)
46N50 Applications of functional analysis in quantum physics
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