Abstract
This chapter aims at providing a survey of the body of scientific literature relevant to Quantum Mechanics (QM) and Information Retrieval (IR). The survey is illustrated with a common notation to fully grasp the contribution of each paper. In particular, the probability aspects of IR and those of QM are emphasized because probability is one of the most important topics of both disciplines.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The reading of this chapter requires some knowledge of Probability and Linear Algebra.
- 2.
Note that tr(|x〉〈x||y〉〈y|)=|〈x|y〉|2, which is 1 when x=y.
- 3.
θ is the angle of the polar representation of the complex number \(a_{0} \bar{b}_{0} a_{1} \bar{b}_{1}\).
- 4.
The canonical basis vector |e i 〉 of a vector space with n dimensions is (0,…,1,…,0)⊤ such that 1 occurs at the i-th position.
- 5.
“Statistical correlation” is meant.
References
Accardi L (1997) Urne e camaleonti. Il Saggiatore, in Italian
Accardi L, Fedullo A (1982) On the statistical meaning of complex numbers in quantum mechanics. Lettere al Nuovo Cimento 34:161–172
Aerts D, Gabora L (2005) A theory of concepts and their combinations II: A Hilbert space representation. Kybernetes 34:176–205
Birkhoff G, von Neumann J (1936) The logics of quantum mechanics. The Annals of Mathematics 37:823–843
Bruza P, Cole R (2005) Quantum logic of semantic space: An exploratory investigation of context effects in practical reasoning. In: We Will Show Them! Essays in Honour of Dov Gabbay, vol 1. College Publications, pp 339–362
Bruza P, Kitto K, Nelson D, McEvoy C (2010) Is there something quantum-like about the human mental lexicon? Journal of Mathematical Psychology 53:362–377
Busemeyer J (2009) Introduction to quantum probability for social and behavioral scientists. In: Bruza P, Sofge D, Lawless W, van Rijsbergen K, Klusch M (eds) Proceedings of the Symposium on Quantum Interaction. Lecture Notes in Computer Science, vol 5494. Springer, Berlin, pp 1–2
Deerwester SC, Dumais S, Furnas G, Landauer T, Harshman R (1990) Indexing by latent semantic analysis. Journal of the American Society for Information Science 41:391–407
Di Buccio E, Melucci M, Song D (2011) Towards predicting relevance using a quantum-like framework. In: Proceedings of the European Conference on Information Retrieval Research (ECIR)
Feynman R, Leighton R, Sands M (1965) The Feynman Lectures on Physics. Addison-Wesley, Reading, MA
Halmos P (1987) Finite-Dimensional Vector Spaces. Undergraduate Texts in Mathematics. Springer, Berlin
Hou Y, Song D (2009) Characterizing pure high-order entanglements in lexical semantic spaces via information geometry. In: Bruza P, Sofge D, Lawless W, van Rijsbergen C, Klusch M (eds) Proceedings of the Symposium on Quantum Interaction. Lecture Notes in Computer Science, vol 5494. Springer, Saarbrücken, pp 237–250
Huertas-Rosero A, Azzopardi L, van Rijsbergen K (2008) Characterising through erasing: A theoretical framework for representing documents inspired by quantum theory. http://arxiv.org/abs/0802.1738, visited on February, 2011
Huertas-Rosero A, Azzopardi L, van Rijsbergen K (2009) Eraser lattices and semantic contents: An exploration of the semantic contents in order relations between erasers. In: Bruza P, Sofge D, Lawless W, van Rijsbergen C, Klusch M (eds) Proceedings of the Symposium on Quantum Interaction. Lecture Notes in Computer Science, vol 5494. Springer, Saarbrücken, pp 266–275
Hughes R (1989) The Structure and Interpretation of Quantum Mechanics. Harvard University Press, Harvard
Kolmogorov A (1956) Foundations of the Theory of Probability. Chelsea, New York, NY
Landauer T (2007) Handbook of Latent Semantic Analysis. Lawrence Erlbaum
Melucci M (2005) Context modeling and discovery using vector space bases. In: Proceedings of the ACM Conference on Information and Knowledge Management. ACM Press, New York, NY, pp 808–815
Melucci M (2008) A basis for information retrieval in context. ACM Transactions on Information Systems 26:1–41
Melucci M (2010) An investigation of quantum interference in information retrieval. In: Proceedings of the Information Retrieval Facility Conference. Lecture Notes in Computer Science, vol 6107. Springer, Berlin, pp 136–151
Melucci M, Sitbon L (2011) Modeling emergent associations of nominal compounds: Ongoing research and preliminary results. http://CEUR-WS.org/Vol-704/, visited on February, 2011
Parthasarathy K (1992) An Introduction to Quantum Stochastic Calculus. Birkhäuser, Basel
Piwowarski B, Frommholz I, Lalmas M, van Rijsbergen K (2010) Exploring a multidimensional representation of documents and queries. In: Acte de la Conférence sur la Recherche d’Information Assistée par Ordinateur, pp 57–60
Rieffel E (2007) Certainty and uncertainty in quantum information processing. http://arxiv.org/abs/quant-ph/0702121, visited on February, 2011
van Rijsbergen K (2004) The Geometry of Information Retrieval. Cambridge University Press, Cambridge
Widdows D (2004) Geometry and Meaning. CSLI
Widdows D, Peters S (2003) Word vectors and quantum logic: Experiments with negation and dijunction. In: Oehrle RT, Rogers J (eds) Proceedings of the Mathematics of Language Conference, vol 8, pp 141–154
Zuccon G, Azzopardi L (2010) Using the quantum probability ranking principle to rank interdependent documents. In: Proceedings of the European Conference on Information Retrieval, pp 357–369
Zuccon G, Azzopardi L, van Rijsbergen K (2009) The quantum probability ranking principle for information retrieval. In: Proceedings of the International Conference on the Theory of Information Retrieval, pp 232–240
Acknowledgements
The work by Massimo Melucci has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement N. 247590.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Melucci, M., van Rijsbergen, K. (2011). Quantum Mechanics and Information Retrieval. In: Melucci, M., Baeza-Yates, R. (eds) Advanced Topics in Information Retrieval. The Information Retrieval Series, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20946-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-20946-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20945-1
Online ISBN: 978-3-642-20946-8
eBook Packages: Computer ScienceComputer Science (R0)