Convex Quantum Logic

TL;DR

This paper explores the convex set of quantum states using quantum logic, revealing new algebraic structures that distinguish quantum from classical mechanics and aid in understanding entanglement.

Contribution

It introduces a novel algebraic framework based on convex subsets of quantum states, connecting it with quantum logic and entanglement characterization.

Findings

Identifies a new algebraic structure for quantum states.

Shows differences between quantum and classical mechanics.

Provides a basis for algebraic entanglement characterization.

Abstract

In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of propositions of quantum logic is shown. This new structure is suitable for the study of compound systems and shows new differences between quantum and classical mechanics. This differences are linked to the nontrivial correlations which appear when quantum systems interact. They are reflected in the new propositional structure, and do not have a classical analogue. This approach is also suitable for an algebraic characterization of entanglement.