On the Lattice Structure of Probability Spaces in Quantum Mechanics

作者：Holik Federico^*; Massri Cesar; Plastino A; Zuberman Leandro

来源：International Journal of Theoretical Physics, 2013, 52(6): 1836-1876.

DOI：10.1007/s10773-012-1277-5

• Entanglement
• Quantum information
• Convex sets
• MaxEnt approach

Let be the set of all possible quantum states. We study the convex subsets of with attention focused on 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.

• 出版日期2013-6