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Therefore, in the closed probability (CP) the probability distribution <math>B</math> can be computed from probability <math>A</math> and conditional probabilities <math>P(B=\beta|A=\alpha)</math>. In quantum probability (QP), the classical Total Probability Formula (FTP) is perturbed by the interference term (Khrennikov, 2010);<ref>Khrennikov A. Ubiquitous Quantum Structure: From Psychology To Finances Springer, Berlin-Heidelberg-New York(2010)</ref> for the dichotomous quantum observables <math>A</math> and <math>B</math> of von Neumann type, i.e. given by the Hermitian operators <math>\hat{A}</math> and <math>\hat{B}</math>, the quantum version of FTP has the form: | Therefore, in the closed probability (CP) the probability distribution <math>B</math> can be computed from probability <math>A</math> and conditional probabilities <math>P(B=\beta|A=\alpha)</math>. In quantum probability (QP), the classical Total Probability Formula (FTP) is perturbed by the interference term (Khrennikov, 2010);<ref>Khrennikov A. Ubiquitous Quantum Structure: From Psychology To Finances Springer, Berlin-Heidelberg-New York(2010)</ref> for the dichotomous quantum observables <math>A</math> and <math>B</math> of von Neumann type, i.e. given by the Hermitian operators <math>\hat{A}</math> and <math>\hat{B}</math>, the quantum version of FTP has the form: | ||
{{:F:Krennikov1a}} | {{:F:Krennikov1a}} | ||
If the interference term is positive, then the QP computation would generate a higher probability than its CP counterpart given by the classical FTP. In particular, this probability amplification underlies the supremacy of quantum computing. There are numerous statistical data from cognitive psychology, decision making, molecular biology, genetics and epigenetics demonstrating that biosystems, from proteins and cells (Asano et al., 2015b)<ref>Asano M., Khrennikov A., Ohya M., Tanaka Y., Yamato I. Quantum Adaptivity in Biology: From Genetics To Cognition Springer, Heidelberg-Berlin-New York(2015)</ref> to humans (Khrennikov, 2010,<ref>Khrennikov A. Ubiquitous Quantum Structure: From Psychology To Finances Springer, Berlin-Heidelberg-New York(2010)</ref> Busemeyer and Bruza, 2012<ref>Busemeyer J., Bruza P. Quantum Models of Cognition and Decision Cambridge Univ. Press, Cambridge(2012)</ref>) use this amplification and operate with non-CP updates. | If the interference term is positive, then the QP computation would generate a higher probability than its CP counterpart given by the classical FTP. In particular, this probability amplification underlies the supremacy of quantum computing. There are numerous statistical data from cognitive psychology, decision making, molecular biology, genetics and epigenetics demonstrating that biosystems, from proteins and cells (Asano et al., 2015b)<ref>Asano M., Khrennikov A., Ohya M., Tanaka Y., Yamato I. Quantum Adaptivity in Biology: From Genetics To Cognition Springer, Heidelberg-Berlin-New York(2015)</ref> to humans (Khrennikov, 2010,<ref>Khrennikov A. Ubiquitous Quantum Structure: From Psychology To Finances Springer, Berlin-Heidelberg-New York(2010)</ref> Busemeyer and Bruza, 2012<ref>Busemeyer J., Bruza P. Quantum Models of Cognition and Decision Cambridge Univ. Press, Cambridge(2012)</ref>) use this amplification and operate with non-CP updates. |
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