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Maps on density operators preserving quantum \(f\)-divergences

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For an arbitrary strictly convex function \(f\) defined on the non-negative real line we determine the structure of all transformations on the set of density operators which preserve the quantum \(f\)-divergence.

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  1. We mention that, as one of the referees pointed out, opposed to the conventions in mathematics, in physics the inner product is usually assumed to be conjugate-linear in its first variable and linear in the second. Accordingly, \(\langle A,B\rangle _\mathrm{HS }\) would be defined as \(\mathrm Tr A^*B\). However, in this paper we follow the common mathematical convention which is going to cause no confusion.


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Correspondence to Lajos Molnár.

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The authors were supported by the “Lendület” Program (LP2012-46/2012) of the Hungarian Academy of Sciences. The first and second author were supported by the Hungarian Scientific Research Fund (OTKA) Reg.No. K81166 NK81402. The second and third author were supported by the TÁMOP-4.2.2/B-10/1-2010-0024 project co-financed by the European Union and the European Social Fund.

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Molnár, L., Nagy, G. & Szokol, P. Maps on density operators preserving quantum \(f\)-divergences. Quantum Inf Process 12, 2309–2323 (2013).

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