Quantum contextuality in classical information retrieval

Year 2018, , 1 - 5, 30.06.2018

Roman Zapatrin

https://doi.org/10.33401/fujma.404385

Cited By: 1

Abstract

Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from multiple sample spaces. The structure of event space formed by overlapping sample spaces is known in quantum mechanics, they may exhibit some counter-intuitive features, called quantum contextuality. In this Note I observe that from the structural point of view quantum contextuality looks similar to personalization of information retrieval scenarios. Along these lines, Knowledge Revision is treated as operationalistic measurement and a way to quantify the rate of personalization of Information Retrieval scenarios is suggested.

Keywords

Quantum entanglement, Non-classical correlation, Information retrieval

References

• [1] L. Accardi and Fedullo A. On the statistical meaning of complex numbers in quantum mechanics. Il Nuovo Cimento, 34(7):161–172, October 1982.
• [2] Luigi Accardi. Axioms for quantum probability. In Quantum Probabilty, volume 73 of Banach Center Publications, page 1. Polish Academy of Sciences, 2006.
• [3] R. J. Greechie and S. P. Gudder. Quantum logics. In C.A. Hooker, editor, Contemporary Research in the Foundations and Philosophy of Quantum Theory, pages 143–173. Reidel, Dordrecht, 1973.
• [4] Matthias Kleinmann, Otfried Guehne, Jose R. Portillo, Jan-Ake Larsson, and Adan Cabello. Memory cost of quantum contextuality. New Journal of Physics, 13:113011, 2011.
• [5] F.W. Lancaster. Information Retrieval Systems: Characteristics, Testing and Evaluation. Wiley, New York, 1968.
• [6] Yeong-Cherng Liang, Robert W. Spekkens, and Howard M. Wiseman. Specker’s parable of the overprotective seer: a road to contextuality, nonlocality and complementarity. Phys. Rep., 506(1-2):1–39, 2011.
• [7] Massimo Melucci. When Index Term Probability Violates the Classical Probability Axioms Quantum Probability can be a Necessary Theory for Information Retrieval.
• [8] Benjamin Piwowarski, Ingo Frommholz, Mounia Lalmas, and Keith van Rijsbergen. Exploring a multidimensional representation of documents and queries. In Proceedings of RIAO, 2010.
• [9] Stephen Robertson. On event spaces and probabilistic models in information retrieval, presented at. In SIGIR 2002 Workshop on Mathematical/Formal Methods in Information Retrieval, 2004.
• [10] Karl Svozil. Quantum information via state partitions and the context translation principle. Journal of Modern Optics, 51:811–819, 2004.
• [11] Karl Svozil. How much contextuality? Natural Computing, Online First(nn):nn–nn, 2012.
• [12] Robert S. Taylor. Process of asking questions. American Documentation, 13:391–396, October 1962.
• [13] Paolo Zanardi. Virtual quantum subsystems. Phys.Rev.Lett., 87:077901, 2001.
• [14] Roman Zapatrin. Factory of realities: on the emergence of virtual spatiotemporal structures. In: ”Beyond Peaceful Coexistence: The Emergence of Space, Time and Quantum”, Ignazio Licata, Ed., World Scientific (2016), pp. 201–220, 2016.