2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95694We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg picture in terms of deformations of the associative product on the space of observables.Accepted for publication in Int. J. Geom. Meth. Mod. PhysQuantum PhysicsHigh Energy Physics - TheoryMathematical Physicstext