Dynamical Vector Fields on the Manifold of Quantum States

Alberto Ibort; Fabio Di Cosmo; Florio M. Ciaglia; Giuseppe Marmo; Marco Laudato

Dynamical Vector Fields on the Manifold of Quantum States

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arxiv 1707.00293 v1 pith:TJVTJIHJ submitted 2017-07-02 quant-ph

Dynamical Vector Fields on the Manifold of Quantum States

Florio M. Ciaglia , Fabio Di Cosmo , Alberto Ibort , Marco Laudato , Giuseppe Marmo This is my paper

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In this paper we shall consider the stratified manifold of quantum states and the vector fields which act on it. In particular, we show that the infinitesimal generator of the GKLS evolution is composed of a generator of unitary transformations plus a gradient vector field along with a Kraus vector field transversal to the strata defined by the involutive distribution generated by the former ones.

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A Lie-Jordan Geometric Formulation of Lindblad Dynamics
quant-ph 2026-07 accept novelty 5.0

Every finite-dimensional GKLS dissipator is the contraction of a universal trilinear map D(X,Y)Z=XZY−½{YX,Z} whose components depend only on the Lie-Jordan structure tensors B and C.