Abstract
Quantum-inspired models have recently attracted increasing attention in Information Retrieval. An intriguing characteristic of the mathematical framework of quantum theory is the presence of complex numbers. However, it is unclear what such numbers could or would actually represent or mean in Information Retrieval. The goal of this paper is to discuss the role of complex numbers within the context of Information Retrieval. First, we introduce how complex numbers are used in quantum probability theory. Then, we examine van Rijsbergen’s proposal of evoking complex valued representations of informations objects. We empirically show that such a representation is unlikely to be effective in practice (confuting its usefulness in Information Retrieval). We then explore alternative proposals which may be more successful at realising the power of complex numbers.
Supported by (**) EPSRC Grant number EP/F014384/ and (***) Zirak s.r.l. (http://www.zirak.it/). The authors are thankful to Peter Bruza, Kirsty Kitto, Massimo Melucci and Keith van Rijsbergen for initial discussion on the use of complex numbers, and to the reviewers for their comments.
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Zuccon, G., Piwowarski, B., Azzopardi, L. (2011). On the use of Complex Numbers in Quantum Models for Information Retrieval. In: Amati, G., Crestani, F. (eds) Advances in Information Retrieval Theory. ICTIR 2011. Lecture Notes in Computer Science, vol 6931. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23318-0_36
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DOI: https://doi.org/10.1007/978-3-642-23318-0_36
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