An alternative to quantum complementarity

Eric Jakobsson

Raquel Galazo García, Irene Bartolomé, Laura Ares +1 more

K. M. Fonseca-Romero, J. G. G. de Oliveira, J. G. Peixoto de Faria +1 more

In two-dimensional systems, predictability and visibility satisfy a complementarity relation, which has been generalized to bipartite systems by including the concurrence. We consider systems in which the two alternatives of a which-state experiment are nonorthogonal states and propose generalized measures of predictability and visibility. Criteria like symmetry under exchange of the alternatives, vanishing visibility when only one of the alternatives is present, and clear operational meaning, favor definitions of predictability and visibility which use a three-dimensional basis, previously employed in the unambiguous discrimination of nonorthogonal states. We derive generalized single-partite and bipartite complementarity relations and find that predictability and visibility do not exhaust the single-partite properties for a nonorthogonal basis. A recent experiment on the quantum-classical border is analyzed using generalized complementarity relations.

Marc E. Carvallo

Introduction: On Issues in Complementarity and Beyond M.E. Carvallo. Part I: Complementarity, Epistemology, and Ontology. 1. Complementarity-Polarity-Dialectic-Autology: A Conceptual Analysis of Opposition and Unity A. Locker. 2. Complementarity as Challenge: Prefigurations in the History of Thinking H. Fischer-Barnicol. 3. Bohr's Idea of Complementarity J. Hilgevoord. 4. Complementarity and Our Knowledge of Nature H.J. Folse. 5. Ontological Implications of Complementarity K.V. Laurikainen. 6. Aspects of Complementarity R. Vallee. Part II: Complementarity: Alternative Views and Applications. 7. The Probability Trees of Quantum Mechanics: Probabilistic Meta-Dependence and Meta-Meta-Dependence M. Mugur-Schachter. 8. Complementarity in Language: Toward a General Understanding L. Loefgren. 9. Language, Incompleteness and Continuous Domains: Considerations of Complementarity of Abstractions H.W. Campbell, D.G. Stuart. 10. The Measurement Problem in Physics, Computation, and Brain Theories H.H. Pattee. 11. On the Double Architecture of the Semantic Memory P. Erdi, T. Groebler, P. Marton. 12. Axiomatic Methods in Science P. Suppes. 13. Complementarity in the Theory of Conversations and Lp G. Pask. 14. A Theory of Bargains in Experience S.M. Lindenberg. Part III: Beyond Complementarity, Beyond Physics. 15. Complementarity or Process? T. Bastin. 16. Can Quantum Computation Provide a Physically Realistic Model of the Self and Its Brain? P.J.Marcer. 17. Non-Locality in Nature and Cognition F.D. Peat. 18. Spontaneity of Consciousness V.V. Nalimov. 19. A Brief Prolegomenon to the Principle of Metaphoricity M.E. Carvallo. Name Index. Subject Index.

Dénes Petz

Anthony Chefles, Stephen Mark Barnett

The least upper bound in Cirel'son's quantum generalization of the local-realistic Bell inequality is intermediate between the local-realistic and general probablistic limits. An alternative derivation of Cirel'son's inequality is presented which sheds light on the role played by complementarity in determining this bound and the fact that it falls short of the general probablistic limit.