Computational complementarity

Cristian S. Calude, Elena Calude, Karl Svozil +1 more

J. J. Hopfield

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.

Elena Calude, Bruce Mills, Lan Mills

Information about the initial state of a nite automaton may be obtained by interacting with it. Some automata display behaviour analogous to quantum complementarity: two pieces of information can be obtained separately, but not in conjunction. Studies of two computational complementarity properties in nite state interactive automata may shed light on the nature of both quantum and classical computation. But, it can be dicult to determine the statistics of its occurrence. This paper introduces the concept of an observation graph of an automaton. The observation graph can be used as the foundation of algorithms for testing in a uniform manner for a variety of complementarity properties. Implementations have been run in practical time on a standard desktop computer examining all 6-state, 2-symbol automata.

Celia Álvarez Álvarez, Mariamo Mussa Juane

Bohr's Complementarity Principle is a core concept of quantum mechanics. In this article, an updated complementarity relation for the wave and ondulatory aspects of a quantum system is presented and discussed. Two interferometric experiments are implemented in one and two qubit circuits and executed on real hardware. The final state density matrices are reconstructed using quantum state tomography and the complementarity relation is tested via direct computation. Results of the executions are presented both graphically and with a mean squared error analysis for a better comprehension.

Ruth E. Kastner