HOLIK Federico Hernan
congresos y reuniones científicas
The Lattice Structure of Probability Spaces in Quantum Mechanics
Conferencia; VIII Jornadas de Fundamentos de Cuántica - VIII Conference on Quantum Foundations; 2018
We study the convex subsets of the set of quantum states with attention focusedon the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes? Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models? approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.