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When to use Quantum Probabilities in Quantum Cognition: a Discussion Catarina Moreira∗ Andreas Wichert† The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community (Busemeyer and Bruza, 2012). These principles have been applied to explain paradoxical situations that cannot be easily explained through classical theory. Quantum principles have been applied in many different domains ranging from cognitive psychology (Busemeyer et al., 2006; Pothos and Busemeyer, 2009; Pothos et al., 2013), economics (Khrennikov, 2009; Haven and Khrennikov, 2013), biology (Asano et al., 2012; Basieva et al., 2011; Asano et al., 2015), information retrieval (Bruza et al., 2009, 2013), etc. In quantum probability theory, events are characterized by a superposition state, which is represented by a state vector comprising the occurrence of all events. The probability of an event is given by the squared magnitude of the projection of this superposition state into the desired subspace. This geometric approach is very useful to explain paradoxical findings that involve order of effects. But do we really need quantum principles for models that only involve projections? In Information Retrieval, for example, how do quantum interference effects emerge under this projective framework? How do we measure the similarity between documents in a quantum-like manner? Do we really need quantum theory when the purpose is just to apply projections between subspaces? In this work, we intend to explore how quantum probability theory has been applied in the different fields of the literature and make a discussion whether this application has advantages towards the existing classical models. Acknowledgments This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013 and through the PhD grant SFRH/BD/92391/2013. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. ∗ Instituto Superior Técnico, INESC-ID, Av. Professor Cavaco Silva, 2744-016 Porto Salvo, Portugal; e-mail: [email protected] † Instituto Superior Técnico, INESC-ID, Av. Professor Cavaco Silva, 2744-016 Porto Salvo, Portugal; e-mail: [email protected] References Asano, M., Basieva, I., Khrennikov, A., Ohya, M., Tanaka, Y., and Yamato, I. (2012). Quantumlike model of diauxie in escherichia coli: operational description of precultivation effect. Journal of theoretical Biology 314, 130–137 Asano, M., Khrennikov, A., and Ohya, M. (2015). Quantum Adaptative Biology: From Genetics to Cognition (Springer) Basieva, I., Khrennikov, A., Ohya, M., and Yamato, I. (2011). Quantum-like interference effect in gene expression: glucose-lactose destructive interference. Journal of Systems and Synthetic Biology 5, 59–68 Bruza, P., Kitto, K., Nelson, D., and McEvoy, C. (2009). Is there something quantum-like about the human mental lexicon? Journal of Mathematical Psychology 53, 362–377 Bruza, P., Zuccon, G., and Sitbon, L. (2013). Modelling the information seeking user by the decisions they make. In Proceedings of the 36th Annual ACM SIGIR Conference : Workshop on Modeling User Behavior for Information Retrieval Evaluation (MUBE 2013) Busemeyer, J. and Bruza, P. (2012). Quantum Model of Cognition and Decision (Cambridge University Press) Busemeyer, J., Wang, Z., and Townsend, J. (2006). Quantum dynamics of human decision making. Journal of Mathematical Psychology 50, 220–241 Haven, E. and Khrennikov, A. (2013). Quantum Social Science (Cambridge University Press) Khrennikov, A. (2009). Classical and quantum-like randomness and the financial market. In Coping with the Complexity of Economics (Springer) Pothos, E. and Busemeyer, J. (2009). A quantum probability explanation for violations of rational decision theory. Proceedings of the Royal Society B 276, 2171–2178 Pothos, E., Busemeyer, J., and Trueblood, J. (2013). A quantum geometric model of similarity. Psychological Review 120, 679–696 2