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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.

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