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Convex Quantum Logic

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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. These 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 and it provides a new entanglement criteria.

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Acknowledgements

This work was partially supported by the following grants: PIP No 6461/05 (CONICET). We wish to thank G. Domenech for careful reading and discussions.

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Authors and Affiliations

  1. Instituto de Física de La Plata (IFLP), Buenos Aires, Argentina

    Federico Holik & Nicolás Ciancaglini

  2. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, Buenos Aires, Argentina

    Cesar Massri

Authors
  1. Federico Holik
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  2. Cesar Massri
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  3. Nicolás Ciancaglini
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Correspondence to Federico Holik.

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Holik, F., Massri, C. & Ciancaglini, N. Convex Quantum Logic. Int J Theor Phys 51, 1600–1620 (2012). https://doi.org/10.1007/s10773-011-1037-y

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