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Abstract: In this work we study the convex set of quantum states from a quantum logicalpoint of view. We consider an algebraic structure based on the convex subsetsof this set. The relationship of this algebraic structure with the lattice ofpropositions of quantum logic is shown. This new structure is suitable for thestudy of compound systems and shows new differences between quantum andclassical mechanics. This differences are linked to the nontrivial correlationswhich appear when quantum systems interact. They are reflected in the newpropositional structure, and do not have a classical analogue. This approach isalso suitable for an algebraic characterization of entanglement.

Author: F. Holik, C. Massri, N. Ciancaglini


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