Convex Quantum Logic

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.

References in corpus (3)

• A general theoretical framework for decoherence in open and closed systems
• A quantum logical and geometrical approach to the study of improper mixtures
• Predicting decoherence in discrete models

Cited by in corpus (8)

• On the lattice structure of probability spaces in quantum mechanics
• Non-deterministic semantics for quantum states
• Non-Hermitian Hamiltonians in decoherence and equilibrium theory
• Dynamics of algebras in quantum unstable systems
• Convex politopes and quantum separability
• Generalized entropies in quantum and classical statistical theories
• Quantal effects and MaxEnt
• Logical structures underlying quantum computing