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Maps on quantum states preserving Bregman and Jensen divergences
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abstract
We describe the structure of the bijective transformations on the set of density operators which preserve the Bregman $f$-divergence for an arbitrary differentiable strictly convex function $f.$ Furthermore, we determine the preservers of the Jensen $f$-divergence in the case when the generating function $f$ belongs to a recently introduced function class called Matrix Entropy Class.
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Wigner symmetries single out symmetric Wasserstein distances in all finite dimensions
Within quadratic costs from ≤ d^{2}-1 observables, Wasserstein isometries are precisely the Wigner symmetries iff the cost is isotropic (a positive multiple of the identity on the traceless subspace).
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