Comments on the holonomy of eigenvector bundles in the vicinity of higher-order exceptional points and on the Lie group structure underlying the embedding of the PTQM brachistochrone into a two-qubit system

On the poster new findings on two different topics are presented --- related separately to geometric (Berry) phases in non-Hermitian quantum systems in higher-dimensional Hilbert spaces and to the specific realization properties of PT-symmetric quantum brachistochrones in two-qubit systems fulfilling the Aharonov-Anandan lower bound on quantum evolution times.
Specifically, in the first part of the poster we present new results on the holonomy properties of eigenvector bundles of non-Hermitian operators which can be mapped into simplest versally deformed n-th order Jordan blocks. (This generalizes earlier considerations on similar setups with 2-dimensional Jordan blocks [1].)
In the second part of the poster, we start from the embedding of the PT-symmetric brachistochrone into a Hermitian two-qubit system (as recently proposed in [2]) and show that the resulting evolution of the two-qubit system is itself a conventional quantum brachistochrone lying exactly on the non-local Lie-group orbit induced by one of the non-trivial entanglement generators.

[1] U. Günther, I. Rotter and B. Samsonov, "Projective Hilbert space structures at exceptional points", J. Phys. A 40, 8815 (2007), arXiv:0704.1291[math-ph].
[2] U. Günther and B. Samsonov, "Naimark-dilated PT-symmetric brachistochrone", Phys. Rev. Lett. 101, 230404 (2008),
arXiv:0807.3643[quant-ph].