Minhyung Cho

Operation continuity of effect algebras

In this paper, we prove that the operations @? and @? of effect algebras are continuous with respect to their ideal topology, and if the effect algebras are lattice effect algebras, then under some conditions, the lattice operations @? and @? are also continuous with respect to their ideal topology.

Field Extension of Real Values of Physical Observables in Classical Theory can Help Attain Quantum Results

Physical quantities are assumed to take real values, which stems from the fact that an usual measuring instrument that measures a physical observable always yields a real number. Here we consider the question of what would happen if physical observables are allowed to assume complex values. In this paper, we show that by allowing observables in the Bell inequality to take complex values, a classical physical theory can actually get the same upper bound of the Bell expression as quantum theory. Also, by extending the real field to the quaternionic field, we can puzzle out the GHZ problem using local hidden variable model. Furthermore, we try to build a new type of hidden-variable theory of a single qubit based on the result.

Decomposition Properties of Quantum Discord

The quantum discord was introduced by Ollivier, Zurek, Henderson, and Vedral as an indicator of the degree of quantumness of mixed states. In this paper, we provide a decomposition condition for quantum discord. Moreover, we show that under the condition, the quantum correlations between the quantum systems can be captured completely by the entanglement measure. Finally, we present examples of our conclusions.

An ideal topology type convergent theorem on scale effect algebras

The famous Antosik-Mikusinski convergent theorem on the Abel topological groups has very extensive applications in measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the ideal topology. This paper shows also that the ideal topology of effect algebras is a useful topology in studying the quantum logic theory.